It comes after the Commissioner for South Yorkshire Shaun Wright refused to step down despite calls to do so from Home Secretary Theresa May.
Mr Clegg told BBC Radio Sheffield Mr Wright should go and the PCC role was a "discredited experiment".
Labour accused Mr Clegg, whose party helped pass legislation to create PCCs, of "classic Lib Dem hypocrisy".
Theresa May is facing calls from MPs for emergency legislation so that PCCs could be forced to leave their job.
Earlier on Friday, Mr Wright again made it clear he will not resign in connection with the Rotherham child abuse scandal.
Mr Wright, who used to head children's services at Rotherham Council before being elected in 2012, has quit the Labour Party but remains as an independent.
Mr Clegg says his call to scrap PCCs is a "personal" view, although his Lib Dem party is already due to vote on an alternative system of police oversight at its conference in October.
Asked about Mr Wright's refusal to quit, Mr Clegg said: "It's just a disgrace saying 'I'm not going to take any responsibility for it.'
"I have to say I've come to my own personal view, I always had huge misgivings about the Conservatives' idea of Police and Crime Commissioners.
"They put it into the coalition agreement - fair enough - that's what you do in a coalition. Parties put in different ideas into the coalition agreement.
"I remember saying to the Tories at the time, 'look, be careful with this, because the last thing you want is just a bunch of recycled politicians, you know, overseeing our police. They said 'no, no, no, you'll get members of the public, you'll get independent-minded folk'.
"And instead what have we got in Shaun Wright and frankly in Police and Crime Commissioners across the north of England is a bunch of recycled Labour politicians who now refuse to actually accept responsibility.
"So I've come to the view that it is now time to scrap this experiment. And I think Shaun Wright has driven the death nail into this short experiment of Police and Crime Commissioners."
The Conservatives distanced themselves from Mr Clegg's call for one of their flagship policies to be scrapped.
A spokesman said: "Police and Crime Commissioners are the link between the people and the police, engaging with local communities to address long-term crime issues so police can get on with their job out on the beat."
The Labour Party is considering whether to scrap PCCs if it wins next year's general election and is thought likely to make an announcement on its policy shortly.
Labour's shadow policing minister Jack Dromey reacted to news Mr Clegg's party was to debate axing PCCs by accusing them of "classic Lib Dem hypocrisy".
"They claim to be on the public's side in wanting to get rid of Police and Crime Commissioners but the truth is they are just as responsible for this policy as the Tories are - they voted for it and supported it all the way. You can't trust a word the Lib Dems say."
Deputy Prime Minister Nick Clegg has called for Police and Crime Commissioners (PCC) to be scrapped.