Mike Tyson's one-man show, Undisputed Truth – or Undisputed Troof, in his lisping, snuffling delivery – is a very weird production. Written by Tyson's third wife Kiki and directed by Spike Lee, it opened Thursday night on Broadway after transferring from Las Vegas. Donald Trump was in the audience, and the baseball star Derek Jeter, and an odd combination of big men with thick necks and skinny hipsters unsure of what to do when Tyson starts throwing the word "faggot" around. To give you an idea: two of the biggest cheers of the night go up for "I didn't rape this woman" and "I lost 150lbs."

Firstly, the show's inbuilt drama – can Tyson carry almost two hours of wordy monologue without a prompter, and the answer is yes. He is slick, articulate and funny, with a broad physical comedy and a wry humour that is totally unexpected. "A Tree Grows In Brooklyn my ass," he says, when describing his rough upbringing in New York's outer borough. Photos flash up on a screen above the stage: of his long dead mother, a "country girl" out of her depth in New York, who drank heavily and let Tyson run wild; of Tyson's "street family", the boys he hung out with, robbing and fighting until, by the age of 12, he had dozens of arrests to his name and going to juvenile detention was "like an episode of Cheers – everyone knew my name".

Muhammad Ali in 1979 / Corbis

And then of his first coach, the legendary Cus D'Amato, who introduced him to boxing and turned his life round. There are references to Tyson's "low self-esteem" and "addiction gene" and an unintentionally poignant photo of Muhammad Ali, who visited the facility when Tyson was inside and who he aspired, and failed, to be like. Cus told his young protegee: "how you fight a fight is how you live your life", which in Tyson's case would sometimes be outside the rules. D'Amato coached him to glory as the youngest heavyweight champion of the world, and, when he died, left the boxer unprotected in a sea full of sharks.

So far so good, and Tyson is charming in this first half of the show, sweating profusely, dabbing his head with a handkerchief and breathing heavily. He engages effortlessly with the audience: "a friend of yours, Don?" he says, when a photo of Mitt Romney flashes up on screen and he teases Spike Lee for shoe-horning in politics.

And then it all goes wrong. He would, said Tyson in the opening sequence, have liked to have called the show "boxing, bitches and lawsuits", eliciting shouts of endorsement from the crowd. More shouts when a photo of Tyson with his first wife, the actor Robin Givens, comes up onscreen. They have been divorced for over 20 years, but Tyson seems not to be over it. "Should I?" says Tyson coquettishly, while Kanye West's Golddigger booms out across the theatre. The crowd goes wild and off he goes.

Slack script

It's not so much that it's offensive; although the wisdom of a convicted rapist making cute jokes about his ex accusing him of beating her up and not knowing the difference between menstrual blood, miscarriage blood and blood from a rape doesn't quite clear under the defense of edgy authenticity. It's more that the script goes slack, Tyson's performance loses its tension and he turns, in this long, long section, into a man shouting on a street corner. Like Alec Baldwin and Charlie Sheen before him, Tyson joins the rank of famous men who mistake ranting about their ex-wives as fuel for art, not therapy.

The one redeeming feature in all this is the account Tyson gives of Brad Pitt, dating Givens at the time of the divorce, freaking out when Tyson confronts him. He refers to the actor as "a broken down, bootleg version of Robert Redford" and then asks him for a job.

After that it's business as usual. The list of women – sorry, whores, bitches and tramps – who have victimised Mike grows. When he revisits his jail term for raping Desiree Washington it's to rehash his defense and question her credibility. No doubt, he says, he owes lots of women an apology. But she isn't one of them. He complains heartily about all the money he has dropped on his girlfriends over the years. He calls himself a "dumb nigger" and says he hates that word: "I wish white people had never invented it."

Then it's on to Don King and more exploitation: when Tyson finally got around to auditing the notorious promoter, he says, he realised he'd been charging him $8,000 a week for towels alone.

He deals swiftly with the Holyfield episode, thanking him for his forgiveness, sincere this time in contrast to the "contrived-ass" apology he gave when the ear-biting episode happened. There's a sentimental section on his eight children and how he could have been a better dad to them. The show ends with a dedication to his late daughter, Exodus.

People will come to the show for the gossip and celebrity, and it is more than that, successfully prosecuting a character in what its makers no doubt consider "taboo-breaking" style. It doesn't break taboos. After the entertainment, what it does, primarily, is remind us how violent men who hate women attract boy crushes from other men who wouldn't dare. When, during the ovation, Spike Lee stands next to Tyson on stage, he looks like the class geek who can't believe the toughest kid in school wants to hang out with him. Well done.