Donald Trump said the 'mess' was a result of their focus on his mishandling of classified information.
Both Trump and Biden are now being investigated by special prosecutors for the material - but Biden on Thursday said 'there's no there there' in a bizarre answer when persistently questioned about the discovery.
Biden said he had 'no regrets' over his handling of classified material - remarks which seem to be coming back to haunt him.
'They created this Documents mess for themselves by being so totally DERANGED about me, and I did NOTHING WRONG!!!' raged Trump on Saturday.
California congressman Darrell Issa mocked Biden's frustrated insistence that he had done nothing wrong.
'I guess there wasn't nothing there there, Mr. President,' he said.
Ted Cruz, a member of the Senate Judiciary Committee, tweeted: 'AGAIN?!? How in the HELL do they keep screwing this up??'
The Texas senator added: 'As Biden repeatedly says, 'everyone knows how seriously I take classified documents.'
'Yes. Yes we do.'