Speaking on Friday, Mr Mann told Sky News that guaranteeing Jewish MPs would stand again would "shut up some of the extremists".
"What Jeremy Corbyn should be doing is leading... 'we've had enough of this intimidation, this bullying, this racism, you are automatically candidates at the next election'. That's what I call leadership... Jeremy get leading."
He said that he himself had once been the subject of a death threat from a Labour member, adding: "Thugs, bullies, extremists, racists... they need throwing out of the Labour Party".
He defended Mr Field as "the key champion against child poverty in the Labour Party over the last 25 years... He's a huge figure in the party, in the country."
Mr Mann's call came as another Labour MP, Mike Gapes, said he was considering resigning over antisemitism in the party.
He told the Evening Standard he would wait to see what happened next week, when the party's governing body will vote on whether to adopt the International Holocaust Remembrance Alliance definition of antisemitism.
The refusal to do this in July sparked a huge row between the party and its Jewish supporters that has raged through the summer.
"I am agonising every day about the situation and the state of the Labour Party," Mr Gapes said.
