Mr Watson and Labour’s former communications director traded blows as they appeared on ITV’s Peston on Sunday.
Mr Campbell blasted the current Labour administration for failing to shut down Theresa May’s approach to leaving the European Union.
He said "none" of Labour's six tests for Brexit were being met in the final deal the Prime Minister is expected to bring Parliament.
“I think the Labour Party should actually follow the logic of that through now, and start campaigning clearly in saying that the Brexit deal she’s bringing back, there’s no way Labour can support it if those tests are to mean anything," he said.
Mr Watson hit back Campbell, saying: “I know you used to be a party sort of communications officer but... we have to listen to the whole of the British people on this... and we’ve got to make sure that we honour them by saying we’re coming out of the EU.”
Tony Blair's former spin doctor retorted: "In which case, what you are saying is whatever happens whatever the cost, whatever the consequences, we’re going to support whatever deal she brings back. That’s crazy, that is crazy."
Mr Watson denied this, adding: "What I’m saying is you no longer decide Labour Party policy. I know you'd like to. I'm sorry about that."
Mr Campbell then said: "I'm happy where I am. I’m not happy with where you’re pretending that you’re doing something different if you’re basically in the same position whatever happens."
The Labour deputy leader later told host Robert Peston he had lost 39 kilograms – by putting butter in his coffee.
Mr Watson, 51, said he was motivated to take better care of his health after reading about Labour politicians who died early.
He said one part of his new regime was Bulletproof coffee – usually made using butter – which is "a way of getting saturated fats into your diet which means you're not as hungry during the day".
"I basically stopped taking sugar, refined sugar, and then I started walking 10,000 steps a day and walking up staircases and when a bit more weight came off I started to jog and cycle," he said.
The West Bromwich East MP, first elected in 2001 said he was the "thinnest I've been" since entering the Commons.