The Liberal Democrat leader accused them of "masochism" and claimed older Brexit voters with views "coloured by nostalgia from an imperial past" had imposed their will on a younger generation more comfortable with the European Union.
Meanwhile, Whitehall sources sought to play down speculation that Theresa May would be prepared to pay a Brexit bill of £36 billion as part of a deal to strike a comprehensive free trade agreement with Brussels.
The so-called "divorce" bill has been one of the main stumbling blocks in Brexit negotiations between the Government and Brussels.
The Sunday Telegraph reported that the Government will only agree to pay the sum if the EU treats it as part of a deal on future relations - including the comprehensive trade agreement sought by the Prime Minister.
The EU's stance is that trade talks cannot begin until significant progress has been made on the financial settlement, citizens' rights and Northern Ireland.
The newspaper quoted a senior Whitehall source as saying the EU's position was that the fee should be 60 billion euro (£54 billion), but the "actual bottom line" was 50 billion euro (£45 billion), the UK's position was 30 billion euro (£27 billion) and "the landing zone is 40 billion (£36 billion) even if the public and politicians are not all there yet".
A senior Government source told the Press Association that "no such figure has been agreed" while another Whitehall source said it was "speculation".
Officials at the Brexit department would not comment on the report but referred to David Davis' acknowledgement that the Government would work with Brussels "to determine a fair settlement of the UK's rights and obligations.
Lib Dem leader Sir Vince's strongly worded attack on Brexit "martyrs" came after a YouGov poll suggested 61% of Leave voters would consider significant damage to the British economy to be a price worth paying for leaving the EU.
Writing in the Mail on Sunday he said: " To describe such masochism as 'martyrdom' is dangerous. We haven't yet heard about 'Brexit jihadis' but there is an undercurrent of violence in the language which is troubling."
Sir Vince, 74, added that the "self-declared martyrs" appeared to be "predominantly elderly".
"The martyrdom of the old comes cheap, since few have jobs to lose," he said.
The housing market, pensions and government policies - including some while he was in the Cabinet - had contributed to a "growing rift" between the generations.
"The old have comprehensively shafted the young. And the old have had the last word about Brexit, imposing a world view coloured by nostalgia for an imperial past on a younger generation much more comfortable with modern Europe," he said.