"And I think I have wasted enough of our viewer's time", the long time host told Miller.
Miller was combative, faked outrage, and demanded Tapper given him three minutes to say whatever he wanted rather than answer questions.
"Because it's my show and I don't want to do that", Tapper jabbed.
After Mr Trump tweeted about having a bigger "nuclear button" than North Korean leader Kim Jong-un, more than 100 medical professionals signed a letter saying they were "deeply concerned" about the President's "psychological aberrations".
"I was a very excellent student, came out and made billions and billions of dollars, became one of the top businesspeople, went to television and for 10 years was a tremendous success as you probably have heard, ran for president one time and won", he said.
Throughout the interview, Miller repeatedly praised Trump's political prowess, knocking the "so-called political geniuses in Washington" who didn't predict the populist Republican's ascent.
The book contains several explosive allegations, particularly from former White House chief strategist and chief campaign executive Steve Bannon, who told Wolff that the meeting between Donald Trump Jr., Trump's son-in-law Jared Kushner and then-campaign manager Paul Manafort and a Russian attorney in the summer of 2016 was "treasonous", and insinuated that Trump had met with the Russians that day. Miller was there to trash the book and its sources, namely Steve Bannon, ousted from the Trump Train and recently spurned by his original patrons, the billionaire Mercers.
"Stephen -" Mr. Tapper cut in.
Trump responds to Michael Wolff's book about his campaign and the early days of his presidency: "I consider it a work of fiction".
Miller accused Tapper of being "condescending" and failing to ask questions about policy.
When Tapper got to the president's mental fitness, Miller turned it into a full-on slap of CNN, saying there was a "crisis of legitimacy" and a "toxic environment" at the network.
Extracts from Fire and Fury have raised questions about Trump's mental health, which in turn led to the former reality TV star to tweet he was a "very stable genius". 'I don't know what magical you're talking about'.
Miller followed up by bashing CNN even more, but Tapper had finally had enough.
Miller tried to protest, but Tapper quickly said, 'Thank you Stephen.' The camera panned away from the White House aide as Tapper started reading from the teleprompter, readying his audience the next segment.
"I get it. There's one viewer that you care about right now and you're being obsequious, you're being a factotum in order to please him, okay?"