"We have a President who does not understand governance," the former Democratic vice president said.
Biden went on to list examples of Trump's public actions since taking office that he viewed as cause for concern, particularly when Trump took to Twitter to dismiss Secretary of State Rex Tillerson's diplomatic efforts on North Korea.
"It is absolutely bizarre," Biden said.
The comments from Biden, who acknowledged a "grace period" of criticism from one administration to the next was typical, came during a scheduled discussion on bridging the partisan divide at a University of Delaware discussion he held with Republican Ohio Gov. John Kasich.
What began as a jovial session on Tuesday afternoon between the two longtime politicians quickly turned into a stern discussion about a modern erosion of norms along with toxic behavior in Washington, which they diagnosed as a result of disconcerting changes in the economy and the slipping decorum in politics.
Throughout the event, Biden rebuked Trump specifically for behavior he argued is unsettling and destabilizing.
He told the audience, "This penchant for self-aggrandizement and this penchant for tweeting, this penchant to focus so specifically and eternally on what he does or doesn't do, even if he was right about everything, is sending a message to all of you and sending a message to your younger siblings that is just totally inappropriate."
Biden said holdovers from the Obama administration call him concerned about the state of the federal government, and he tells them: "Please stay."
Biden cited a moment earlier this year where Trump pushed aside
the prime minister of Montenegro, which Biden characterized as being followed by Trump thrusting his chest and chin forward as he emerged in front of the European politician. Biden said the moment made him think of "Il Duce," a term for the Italian fascist dictator Benito Mussolini.
"Not a joke," Biden said. "Not a joke. That's what people are thinking. That's what people are thinking. Violating the norms of personal conduct generates more anxiety and fear than any policy prescription that this President has enunciated."
A broken system
Biden and Kasich both were outspoken critics of Trump during the campaign season from opposite sides of the aisle, and since the election, the two have pushed back against their own parties for what they view as improper moves away from the political center.
Without pointing to Trump, Kasich said the political problems of the day manifested from years of misbehavior on both sides and a tendency for each party to play toward its own base.
"It's become about base politics," Kasich said. "It's the base politics of Republicans, and it's the base politics of Democrats."
Biden concurred, calling the political system "broken" and warning that the growing ideological divide made it more difficult to achieve any agreement.
"The center is shrinking," Biden said. "And that doesn't mean the center, per se, is good. But god, how can you run this country without reaching a consensus?"