Witnesses said a man carrying two knives was Tasered by police after running from the discount shop in Bury Street, Abingdon, at about 11:20 GMT.
Staff at a nearby Spar store said they barricaded themselves inside as the man tried to gain entry, before he was restrained by the police.
A 36-year-old man, who is from Abingdon, has been arrested on suspicion of murder.
Updates on this story and more from Oxfordshire
Police said the deceased was yet to be identified and his next of kin had not yet been informed.
Kash, who works at the Spar shop, said after the stabbing a man tried to push his way into the store.
He said: "He approached with two knives in his hands and he tried to enter. He said 'I just want to shake your hand' and we held the door closed.
"Then a policewoman caught up with him and Tasered him."
Poundland chief executive Jim McCarthy said he was "shocked" that one of the company's customers had been killed.
He said: "Our sympathy and thoughts centre on the family of the deceased and of course with other customers and colleagues who were in the store at the time of this terrible incident."
Supt Rory Freeman said: "Members of the public will understandably be shocked and upset by this incident today, which has happened in a very public place.
"At this stage, this is not being treated as a terrorist incident."
A second man nearby suffered a minor injury to his thumb. Thames Valley Police are investigating whether the incidents were connected.
Joanna posted on Twitter: "Watching everything that happened today in Abingdon from my office window was terrifying. Rest in Peace."
The leader of South Oxfordshire District Council John Cotton said on Twitter it was "dreadful news" and praised the quick response by police.
A local trader, who did not want to be named, said: "People are absolutely devastated. Normally it's a very busy vibrant market, but everyone has gone home."
Thames Valley Police has appealed for anyone who captured footage at the scene to come forward.Martin Hamilton's body was discovered by a dog walker in woodland near West Calder on 17 December.
The 53-year-old, who was from Glasgow, was released from prison in September 2014 but was sought by police in April for breaching the terms of his licence.
Police described him at the time as "potentially dangerous". His death was being treated as unexplained.
Hamilton was nicknamed the Blackhill Butcher, after the Glasgow housing estate from which he operated.
He had been on the police's most-wanted list before he was jailed in 2000 over a string of charges including drug dealing, torture, abduction and sodomy.
Hamilton was sentenced to a minimum of nine years in prison after being found guilty at the High Court in Inverness.
The case was moved 200 miles from Glasgow amid fears that witnesses could be intimidated. Hamilton had evaded justice on 12 previous occasions when witnesses were too terrified to testify.
In court, a sickening picture emerged of how Hamilton, also known as the Fat Controller, entrapped young men with offers of drugs.
Two young drug addicts were imprisoned in a Glasgow flat, stabbed through the cheek and had boiling water poured over them.
Another attack in Edinburgh included an attempt to cut off a victim's finger.
Passing sentence, judge Lord Kingarth said: "You showed yourself capable of taking sadistic pleasure in the infliction of pain and the inspiration of real terror over long periods. You pose a substantial danger to the public."
When Police Scotland issued an appeal to find Hamilton in April they said he may be dangerous and urged members of the public not to approach him. A further appeal was made in June.
In October, an appeal was made on the BBC's Crimewatch programme and the Crimestoppers charity also offered a reward of Â£2,000 for information leading to his arrest.
Det Supt Kenny Graham said the site near West Calder where the remains were found would stay closed off or several more days "whilst we complete further searches and specialists carry out their work".
The nearby B7105 will also remain closed.
Det Supt Graham said: "My condolences go out to the family of Martin Hamilton, who have had to receive such devastating news so close to Christmas.
"A team of officers is dedicated to this inquiry, so we can seek to give them answers as quickly as possible.
"We are continuing to conduct examinations with various scientific experts to establish exactly when and how Mr Hamilton died, and to ensure any evidence available can be captured from the scene and from the remains themselves."While opinion is divided, Mrs Clinton is largely thought to have come out on top in Sunday's debate in St Louis. But columnists raised the issue of her failure to tackle Mr Trump effectively, allowing him to "exceed expectations".
"The smiling Hillary we saw throughout the first debate on Long Island? She didn't make the trip west."
Fox News concludes that Mr Trump managed to pull off a surprising performance, although the news channel does not explicitly state that the Republican candidate won the debate.
The conservative network says he performed well, pivoting and manoeuvring through questions, allowing him to save his presidential hopes.
Political analyst William Whelan said the night fell into the hands of Mr Trump.
He said the Republican defended his record and unlike the first debate, when he was often blown off course by the former secretary of state and "torpedoed by his own badgering performance", he improved as the night went on.
Mr Trump's decision to launch a blistering attack against Hillary Clinton and her husband is described by Fox as the equivalent of "Hillary dropping Alicia Machado on Trump" in the previous debate.
That was the line used by Breitbart news, which is in a minority in handing the title to Mr Trump.
In a leading story quoting comments from former mayor of New York City, Rudy Giuliani, it reports that Mrs Clinton was "pounded on bad decisions".
It refers to accusations from Mr Trump that Mrs Clinton and the Democratic Party helped "create the vacuum in the Middle East" that allowed so-called Islamic State to form.
The hard-right news website, whose executive chairman Stephen Bannon was appointed Mr Trump's campaign chief in August, is running its own readers' poll, the results of which have yet to be announced.
The site also highlights support from Republican vice-presidential nominee Mike Pence, who said in a tweet that he was proud of Mr Trump and congratulated him on "a big debate win", while ending it with a shortened form of Mr Trump's 'Make America Great Again' slogan.
"All Hillary Clinton had to do was remain upright for 90 minutes."
The Washington Post's verdict is that the debate highlighted an "increasingly isolated" Mr Trump during an "unusually dark and bitter face-off". Over the past year, the newspaper has been at the forefront of investigations into Mr Trump, and has published several editorials condemning the candidate.
On the news site's Right Turn blog, Jennifer Rubin says Mrs Clinton had very little to do in order to go "the last little way in wrapping up the election".
She writes that Mrs Clinton handled the audience well when answering questions, adding that the former secretary of state effectively won the debate early on by "simply keeping her cool".
Issues ranging from Mr Trump's tax payments to his foreign policy have, according to the Post, given Mrs Clinton plenty of material for a new raft of political ads.
In a separate piece for the Post, opinion writer Eugene Joseph Dionne Jr writes that Mr Trump's "petulant" and "boorish" approach on the night was an indication of "a man aware that his campaign was at the edge of extinction".
"It took the nastiest, most bitterly personal presidential debate in recent memory for the Republican nominee to stanch the downward plunge" - so writes Stephen Collinson for CNN.
He says that Mr Trump will live to fight another day "after throwing out a battery of vicious counter punches", while US politics "changed in the course of one nasty night".
Meanwhile a CNN/ORC poll of debate watchers handed Sunday's victory to Mrs Clinton. But the results also showed that Mr Trump managed to exceed expectations.
Mrs Clinton took the win with 57% of the vote, the poll says, while Mr Trump managed to achieve 34%. The result could be considered a disappointment for Mrs Clinton, who scored 62% in the first presidential debate.
The Atlantic, which endorsed Mrs Clinton last week, suggests that Mr Trump suffered an "implosion" in St Louis on Sunday.
Ron Fournier, whose coverage of US politics dates back to the days of Bill Clinton, writes that Mrs Clinton did about as well as anyone could while dealing with a "barking" opponent and "pouting menace".
Mr Fournier said that throughout the debate the controversial Republican "failed to patch together his collapsing campaign".
The website suggests that Mrs Clinton perfectly handled Mr Trump's comment about "instructing my attorney general to get a special prosecutor" to look into allegations that she deleted thousands of emails in violation of a congressional subpoena.
Mrs Clinton laughed and said it was a good thing "somebody with Donald Trump's temperament" doesn't have such power.
"Nothing hurts a bully like somebody laughing at him," the column says.A "concrete plan" was in place for the operation over the eastern city of Deir al-Zour, said Jan Egeland, who chairs a humanitarian taskforce.
Convoys of UN trucks on Wednesday began delivering much-needed aid to 80,000 people in five other besieged areas.
The UN says 200,000 residents remain besieged in parts of Deir al-Zour.
"It's a complicated operation and would be in many ways the first of its kind," Egeland said of the air drops.
The UN will work with the Syrian Arab Red Crescent and other local groups to drop aid by parachute for distribution, World Food Programme spokeswoman Bettina Luescher said.
She did not specify when the air drops would begin but said a single aircraft would be used initially.
The World Food Programme had previously ruled out humanitarian air drops in Syria due to the complexities of obtaining use of airspace, organising distribution on the ground, and finding suitable drop zones.
The UK government also said air drops were "high risk and should only be considered as a last resort when all other means have failed".
But Egeland said the strategy was the only way to feed people in Deir al-Zour.
"It is either air drops or nothing. Air drops are a desperate measure in desperate times," he told Reuters.
Speaking after a meeting of the 17-member International Syria Support Group (ISSG), he also said that UN aid was expected to reach all of Syria's 18 besieged areas within a week.
The UN believes more than 480,000 Syrians are living in besieged areas, with four million more people in so-called "hard-to-reach" areas.
All parties to the conflict are believed to have used siege warfare - where military forces surround an area and cut off essential supplies - in breach of international law.
On Wednesday, aid trucks reached rebel-held Muadhamiya and Madaya, near Damascus, and pro-government northern villages of Foah and Kefraya. Another town, Zabadani, was reached later.
The supplies, which included some medical supplies, are expected to last for about a month.
The deliveries were part of an agreement approved by the ISSG that world powers hope will lead to a "cessation of hostilities" by Friday.
The agreement does not apply to the fight against IS or al-Nusra Front, an al-Qaeda affiliate, and offensives by Syrian government forces and Kurdish militia fighters on rebel-held areas of the northern province of Aleppo have dimmed hopes of a truce.
A new report from humanitarian group Doctors Without Borders/Medecins Sans Frontieres (MSF) says 1.9 million people are under siege in Syria. It said data from hospitals and clinics it supports recorded 154,647 war-injured people and 7,009 war dead in 2015, 30 to 40 percent of whom were women and children.
The data, MSF said, showed "civilians and civilian areas continued to be devastated" by the conflict.
A strike on an MSF-supported hospital in Idlib province on Monday killed 25 people, the group says.
"Permanent members of the UN Security Council, four of whom are actively involved in the war in Syria, must answer for their failure to uphold their most basic responsibilities toward civilians," said MSF president Dr Joanne Liu.Sadie Hartley, 60, was stunned with a cattle prod and stabbed at her home in Helmshore, Lancashire, in January.
Preston Crown Court heard Sarah Williams, 35, exchanged naked photographs with Ms Hartley's partner Ian Johnston in the weeks prior to the death.
Ms Williams denies murder.
The court has heard Ms Williams was obsessed by Mr Johnston, 57, and "eliminated" Ms Hartley with the help of Katrina Walsh, 56,  who also denies murder, when he refused to leave her.
Mr Johnston, who had been in an "intermittent", "intimate" relationship with communications director Ms Hartley, began a sexual relationship with Ms Williams after they met in December 2012.
The former firefighter told Ms Williams the relationship was over months later, he said, but she kept contacting him in person or by text and even sent an anonymous letter to Ms Hartley, boasting the sender had had "fantastic" sex with Mr Johnston.
John McDermott, prosecuting, said Mr Johnston and Ms Williams exchanged naked photographs on 3, 4 and 5 December last year.
Mr Johnston said he didn't block the messages and responded "in kind" to Ms Williams' messages.
But he told the prosecutor he did not seek to rekindle the relationship and was "distraught" when he read the texts the next day.
There were further similar exchanges between the pair on Christmas Day, and again 10 days before the murder, Mr McDermott told the court.
Mr Johnston had been in Switzerland when the messages in January were sent, the court heard.
Mr McDermott asked: