A campaign rally audience laughed as Mr Trump ran through a list of what he described as holes in Christine Blasey Ford’s appearance before the US Senate Judiciary Committee.
She testified that Mr Kavanaugh pinned her on a bed, tried to take off her clothes and covered her mouth in the early 1980s when the two were teenagers.
Mr Kavanaugh has denied Ms Ford’s allegations.
“How did you get home? ‘I don’t remember,’” Mr Trump said imitating Ms Ford at the rally in Southaven, Mississippi.
He added: “How did you get there? ‘I don’t remember.’ Where is the place? ‘I don’t remember.’ How many years ago was it? ‘I don’t know. I don’t know. I don’t know.’”
Imitating her, he said: “But I had one beer - that’s the only thing I remember.”
It marked the sharpest criticism by Mr Trump of Ms Ford since she came forward publicly with the allegation last month.
He had previously called her a “very credible witness”.
Ms Ford’s lawyer, Michael Bromwich, called Mr Trump’s attack “vicious, vile and soulless”.
“Is it any wonder that she was terrified to come forward, and that other sexual assault survivors are as well?” Mr Bromwich tweeted.
“She is a remarkable profile in courage. He is a profile in cowardice.”
The president was in Mississippi on Tuesday looking to use his influence to sway the outcome of a low-profile election that could tip the balance of the Senate.
All signs suggest Democratic women are energised by opposition to Mr Trump’s presidency and the primary season yielded record numbers of female candidates.
The message from Mr Trump and his allies looks to channel the frustration and anxieties of the party’s core voters - white men - just weeks before an election.
The president said: “It’s a very scary time for young men in America when you can be guilty of something that you may not be guilty of. You can be somebody that was perfect your entire life and somebody could accuse you of something ... and you’re automatically guilty.”
Mr Trump also pretended to be a son asking his mother how to respond to an accusation.