Trump is "the bully I knew my whole life," Biden told CNN in an interview. "He's the bully I've always stood up to."
Biden was asked how Democratic voters can have confidence that he's up to taking on Trump when he had trouble sparring in last week's debate against party rivals.
"I don't think I'm having trouble sparring. It's how you want to spar," Biden said. "This is ironic. I've never been accused of not being able to spar. I've been accused of being too aggressive."
Biden said he would beat Trump by "pointing out who I am and who he is and what we're for and what he's against."
"This guy is the 'divider-in-chief,'" said Biden, who added he will "fight without being personal" in this campaign.
"I think the American public want a president with some dignity who has a value set who is actually trying to restore the soul of this country," argued Biden, who remains the front-runner for the 2020 Democratic presidential nomination.
However, Biden's early wide lead has narrowed considerably since rival Sen. Kamala Harris, D-Calif., called him out in the June 27 debate over issues of race, including busing and comments about working with segregationist senators earlier in his career.
Biden said he did not rewatch the debate and he's not worried about how he's perceived: "People know who I am."
In Friday's CNN interview, Biden also called himself a "center-left," suggesting that being moderate is the way to beat Trump. "What I've seen around the country is the vast number of Democrats are where I am on the issues."
Biden said the Democratic Party "is not way left," referring to other candidates in the crowded Democratic field without mentioning any names.
On the issue of who he would pick to be his vice president should he get the Democratic nomination, Biden said it's "presumptuous" to talk about it at this stage.
He did say it would be great to have a female running mate but refused to answer whether Harris would still be on his list.