The quizzer - known as The Beast - says the long-running BBC quiz is well past its sell-by date and should no longer be on the box.
He feels his ITV teatime quiz show The Chase is much more popular - and that John Humphrys' black chairs aren't needed in 2020.
Mastermind has been running since 1972 but speaking to Express.co.uk, Mark says he would bin it off if he was in charge.
"If I could axe anything I would chop Mastermind into tiny pieces," he said.
"I could go to town on why it’s terrible. You have to take it on trust that they try to make the questions fair and balanced in terms of how difficult they are."
Mark also revealed his guilty TV pleasure.
"That's RuPaul’s Drag Race," he said in the Q&A. "It’s the best produced reality show on telly by a mile.
"The challenges are original and it’s consistently funny. If there were a celebrity version I’d do it. I'd be fabulous. I'm 6ft 7 and in heels, I’d be the world’s first seven feet drag queen."
Mark said accepts he needs to be more up-to-speed on Downton Abbey - so is using his spare time to study the show.
Questions on the period drama can catch him out and he confirmed he is also swatting up on cop series Line Of Duty.
But will we be seeing him on another show soon?
He admitted recently that it's a matter of time before he enters the I'm A Celebrity jungle.
"I'm going to do it, it's just a question of when - I am not joking you guys, cannibalism may be on the cards," he told MirrorOnline.
"I would be that hungry and some minuscule pipsqueak mucks up the food challenge and says, 'Oh it doesn't matter, we'll go without for a day', and I will be looking at them going, 'Oh, there's a couple of steaks on that'."
It has the making of a camp classic!