Trump told the Rupert Murdoch-owned newspaper he had advised May on how to conduct Brexit negotiations, "but she didn't listen to me".
May insisted her plan was exactly what Britons had voted for in a 2016 European Union membership referendum.
"I guess when they put out blimps to make me feel unwelcome, no reason for me to go to London".
"The people voted to break it up, so I imagine that's what they'll do".
Referring to the Brexit blueprint, which was outlined by the government on Thursday, he said: "The deal she is striking is a much different deal than the one the people voted on".
It comes just days after Trump declined to say whether May should remain in post, said he had "always liked" Boris Johnson, who quit as foreign secretary over the Chequers agreement, and described the United Kingdom as being in "turmoil".
"I actually told Theresa May how to do it but she didn't agree", he said.
"There will be no alliance more important in the years ahead", she said. We need to rise to the challenge and grasp the opportunities'.
Despite the welcome from May, many Britons are opposed to Trump's visit.
But Johnson, a leading Brexit campaigner, said following European Union rules without being able to alter them risked consigning Britain to the "status of colony", and said it looked like a "semi-Brexit".
Gowdy to Strzok: 'I Don't Give a Damn What You Appreciate'
Strzok and others inside the Federal Bureau of Investigation and DOJ turned our system of justice on its head", he said. She noted, however, that Strzok appeared to give "some conflicting testimony" regarding that particular text message.
It "delivers on the instruction we delivered loud and clear from the British people to take back control", he added.
Outside the mansion, near Oxford to the northwest of London, a couple of thousand demonstrators lined the road and booed Trump's arrival, one of over 100 protests police expect to take place during his four-day trip.
The Scottish Secretary said he would rather MPs were focused on selling the deal to European leaders.
"From the public, the welcome will be far from warm", he told lawmakers on Wednesday, noting there would be protests across the country against Trump's "abysmal record on human rights, his repugnant attitude toward women and his disgusting treatment of minorities".
The publication came after Mr Trump and First Lady Melania Trump arrived in England, hours after meeting Ms May at a lavish dinner to mark his first visit to Britain as U.S. president, amid multiple protests across the country.
The biggest protests are set for Friday, when demonstrators plan to march through central London and float a huge balloon depicting Mr Trump as a baby in diapers over the Houses of Parliament.
And for data protection, the United Kingdom tried to sell it as beneficial to the European Union, noting that the Information Commissioner's Office is an "internationally respected, influential and well-resourced regulator".
May was hosting Trump at a black-tie dinner at Blenheim Palace, birthplace of Britain's World War II Prime Minister Winston Churchill - the leader who coined the term "special relationship" for the trans-Atlantic bond. This would permit "only paid work, in limited and clearly defined circumstances, in line with the current business visa policy", the white paper said.
While insisting that he thinks May is a nice person, President Trump dismissed a report from The Washington Post that he thinks of the prime minister as "a bossy schoolteacher". These will focus on relations with Russian Federation, trade, Brexit and the Middle East.
She said: "There's nothing satisfactory about leaving the European Union, and this document falls far short of what Scotland needs, and it falls short of what our economy needs".
He is then due to spend two days at golf courses he owns in Scotland before travelling to meet Russian President Vladimir Putin.