The Lib Dem leader told thousands of pro-EU demonstrators gathered in Parliament Square that Theresa May's pursuit of a hard Brexit "made Nigel Farage look like a moderate".
But he reserved his most stinging criticism for Mr Davis, who will lead the UK's EU divorce negotiations once Article 50 is triggered this week.
"We believe that that deal, which is being stitched up in the modern-day equivilent of smoke-filled rooms in Westminster and principally in Brussels, to be imposed on the British people, will be the worst affront and assault to democracy imaginable," he said.
"You don't know what that deal will look like, I don't know what that deal will looks like, Therea May doesn't know what that deal will look like and David Davis hasn't got a clue," Mr Farron said, to loud applause from Remainers.
He then suggested the Conservative politcian was out of his depth against Brussel's chief Brexit negotiator Guy Verhofstadt, a former Belgian Prime Minister and senior member of the European Parliament.
"David Davis against Guy Verhofstadt? Guy Verhofstadt will eat him for breakfast," he said.
Mr Davis came in for criticism after he admitted his department had not carried out any economic assessment into the imapct of Britain leaving the EU without a deal.
Describing the action his own Exiting the EU department is taking to prepare the UK for that possibility, the Tory minister told the House of Commons Brexit Select Committee he was not yet able to “quantify” the impact of no Brexit deal being agreed.
Mr Farron also called for the final sign off on the Brexit deal to be given to the people, and expressed solidarity and love to everyone who voted Leave.
"We respect that," he said. "We do not belive for one minute they signed up to that narrow world view Theresa May has chosen.
"She does not speak for the 52 per cent – she barely speaks for the five per cent."
Davis v Verhofstadt is due to begin next month
Tim Farron says David Davis 'hasn't got a clue' over Brexit
Thousands of demonstrators had joined Saturday's Unite for Europe march, starting in Park Lane and ending in a rally in Parliament Square.
The march coincided with the EU's 60th anniversary celebrations in Rome, where leaders of the other 27 member states will gather to discuss plans for the future of the union without the UK.
The protestors who gathered for the rally were greeted by the sight of hundreds of floral tributes to the victims of Wednesday's terror attack, where four people died.
Other speakers included Lib Dem former deputy prime minister Nick Clegg, Labour MP David Lammy and Green co-leader Jonathan Bartley