In extraordinary comments on British politics, Trump also said former foreign minister Boris Johnson, who resigned this week over the Brexit plan and is seen as a potential challenger to May.
"If they do a deal like that, we would be dealing with the European Union instead of dealing with the UK, so it will probably kill the deal," said Trump, who began a four-day visit to Britain on Thursday.
In extraordinary comments on British politics, Trump also said former foreign minister Boris Johnson, who resigned this week over the Brexit plan and is seen as a potential challenger to May, would make "a great prime minister".
He added that London Mayor Sadiq Khan, who authorised protesters to raise a giant balloon showing a nappy-wearing Trump next to the British parliament on Friday, was doing a "terrible job" in fighting crime.
Trump told the tabloid, Britain's best-selling newspaper, that he would have gone about Brexit in a different way.
"I would have done it much differently. I actually told Theresa May how to do it but she didn't agree, she didn't listen to me. She wanted to go a different route.
"I would actually say that she probably went the opposite way. And that is fine. She should negotiate the best way she knows how. But it is too bad what is going on".
Referring to the plan outlined on Thursday in which Britain would aim to keep strong ties in trading of goods with the EU, he said: "The deal she is striking is a much different deal than the one the people voted on.
"It was not the deal that was in the referendum. I have just been hearing this over the last three days. I know they have had a lot of resignations. So a lot of people don't like it," he said.
May is facing a rebellion by Brexit hardliners over the proposals, including the resignation of Johnson and Brexit minister David Davis.
Asked about Johnson, Trump said: "I was very saddened to see he was leaving government and I hope he goes back in at some point. I think he is a great representative for your country."
"I think he would be a great prime minister. I think he’s got what it takes," he added.
Asked about Khan, a member of the opposition Labour Party, Trump was highly critical of the London mayor.
"Take a look at the terrorism that is taking place. Look at what is going on in London. I think he has done a very bad job on terrorism.
"I think he has done a bad job on crime, if you look, all of the horrible things going on there, with all of the crime that is being brought in," he said.
Referring to planned protests on Friday, Trump added: "I think he has not been hospitable to a government that is very important. Now he might not like the current president, but I represent the United States".