The comedian also brought up part of the book in which Trump mocks Attorney General Jeff Sessions, an Alabamian, by calling him "this dumb Southerner".
Mattis is described as among those in the administration who grew exasperated with Trump's limited intelligence; he complained that Trump has the understanding of a "fifth- or sixth-grader", according to Woodward.
Woodward warned the president that it was a "tough" book.
"No, it's - it's going to be accurate, I promise", Woodward said.
After Trump said "both sides" at the Charlottesville white supremacist rally were to blame for the violence that occurred in August 2017, advisers urged him to make another speech condemning white supremacists and neo-Nazis.
If his book is any indication, Woodward probably thinks Mr Trump will need all the luck he can get.
Separately in the book, Kelly is reported to have frequently lost his temper, and described Trump as "an idiot".
While both men refuted remarks attributed to them, Trump took it upon himself to function as a press office with multiple retweets, including retweeting his press secretary's statement.
"'So it sounds like you're on the fence about going to prom with me?'"
The book quotes U.S. defence secretary Jim Mattis as calling Trump a fifth-grader.
President Uhuru leaves for China-Africa summit
China has established 54 Confucius Institutes and 27 Confucius classrooms in 41 African countries. But he added that China and Africa should work towards a more balanced trade relationship.
Rachelle Ann Go meets Prince Harry and Meghan Markle
Markle lived in Toronto when filming TV show " Suits " as an actress. Kensington Palace told HuffPost it wouldn't comment on the matter.
Khalil Mack trade gives Raiders reason to second-guess gamble on Jon Gruden
This contract exceeds the six-year, $135 million deal Los Angeles Rams defensive lineman Aaron Donald received just a day before. With his speed and power, Mack gives the Bears a huge threat on the edge to go with Leonard Floyd on the opposite side.
Mr. Trump slammed the book as "discredited" on Twitter Tuesday and argued quotes were "made up frauds".
The book says Trump's former lawyer in the Russia probe, John Dowd, doubted the president's ability to avoid perjuring himself should he be interviewed in special counsel Robert Mueller's investigation into Russian election interference and potential coordination with Trump's campaign. Johnny Isakson of Georgia said, according to The Post.
Mr Dowd, in a statement, said "no so-called "practice session" or "re-enactment" took place, and denied saying that Mr Trump was likely to end up in an orange jumpsuit.
Mr Cohn allegedly was "appalled" by a draft letter formalising America's withdrawal from a trade agreement with South Korea and so "stole it" from Mr Trump's desk.
Defense Secretary Jim Mattis replied that the administration was trying to prevent World War III. "He made this up to divide!" the US President said in the first of his tweets on the subject just before midnight Wednesday.
"Well, accurate is that nobody's ever done a better job than I'm doing as president", Trump responded.
Woodward says the 448-page book, set to be released next Tuesday, cites mostly anonymous sources.
Mr Cohn, who tried to rein in Mr Trump's protectionist impulses, also planned to remove a similar memo that would have withdrawn the United States from the North American Free Trade Agreement with Mexico and Canada, Woodward wrote.
"Let's [expletive] kill him!" He added that the author "never called me". I never spoke to him. Wolff's book attracted attention with its vivid anecdotes but suffered from numerous factual inaccuracies. Woodward, who helped break the Watergate scandal over 40 years ago, is still a highly respected Washington journalist.
Woodward's book was already ranked the top-selling book on Amazon on Tuesday.