Mr Cable, set to take over on Thursday, has promised constructive opposition instead.
His comments come after the Prime Minister appealed for opposition parties to “contribute, not just criticise”.
However, Mr Cable said: “Our current party leader said he was going to make hell. My approach is more constructive opposition. I don’t think being negative just for the sake of being negative is the right approach. We have got to treat it seriously.”
On Mrs May’s offer, he said: “The idea of finding common ground on particular issues with them, and indeed with Labour… I would be up for that.”
But he suggested that even Conservative voters would balk at the so-called Henry VIII clauses, designed to give ministers huge amounts of power, contained in the Bill.
Dating back to a 1539 law allowing the monarch to govern by proclamation, they could see up to 1,000 “corrections” made to EU laws with MPs offered a vote on only some of them.
He predicted that the move would concern “a lot of people in the Tory Party who are not necessarily Remainers but will worry about what is a very undemocratic model”.
Mr Cable also said he was sympathetic to some of the arguments for Brexit and that the EU needed reform.
The Twickenham MP was hit by controversy recently after he suggested the Brexit voters he had met while campaigning in the referendum were elderly people worried about 80 million Turks “coming to their village”.
But on Brexit, he said: “There are legitimate criticisms of the EU and the way it functions. People who defend it as a finished product are wrong.”
The 74-year-old, the only candidate standing to replace Mr Farron, 47, dismissed suggestions he was too old for the job: “People are as old as they feel and I feel quite young in spirit.”
Brexit Secretary David Davis has issued a rallying cry for everyone to “roll up their sleeves” and get on with the business of Brexit ahead of the resumption of Euro talks tomorrow.
Cabinet minister Liam Fox also warned opposition parties that wrecking the Repeal Bill will only make a “hard” Brexit more likely.
But Scottish First Minister Nicola Sturgeon and Welsh First Minister Carwyn Jones have threatened a constitutional crisis over the legislation.
Yesterday former PM Tony Blair was branded a wolf in sheep’s clothing after claiming the EU could give the UK more control over immigration in return for cancelling Brexit.
But Labour MP Frank Field said voters should not believe “those people who are set on destroying our attempts to leave, who are now appearing as wolves in sheep’s clothing”.