"My job is to go out and make the case why he doesn't deserve to be president of the United States for another four years," Biden said.
The latest prime-time debate featured just seven of the 15 Democrats still in the contest six weeks before the first nomination ballots are cast in Iowa.
Senator Bernie Sanders, second in the standings, blasted Trump as "running the most corrupt administration in the modern history of this country".
The president has "sold out" working families, Sanders added.
But the liberal icon also appealed to conservatives, saying he believes they, too do not want a president with the "temperament" that has led him to dishonour the office.
Trump was impeached in the Democratic-controlled House of Representatives on Wednesday for abuse of power and obstruction of Congress. One day later, the spotlight was already swinging to the Senate trial, where the the president is expected to be acquitted by his Republican majority.
Biden himself is a key figure in the impeachment saga, which centers on Trump's attempts to pressure the president of Ukraine to investigate the former vice president and his son Hunter -- which Democrats said amounted to soliciting foreign interference in next year's vote.
There has been no evidence of wrongdoing by the Bidens.
"This is a global Watergate," Senator Amy Klobuchar said, referring to the scandal that sank president Richard Nixon in the early 1970s.
Trump has blocked key officials in his administration from testifying in the inquiry.
But Klobuchar said that if Trump feels they could exonerate him, "why doesn't he have all the president's men testify?" The showdown marks a significant drop from the 10 candidates in November's debate, and the dozen who crowded the stage in October.
Cozier quarters allowed for more extended exchanges about policy between participants hoping for their party's nomination to challenge Trump.
While the attacks on Trump landed hard, some candidates urged optimism to ease the exasperation many voters have expressed about American politics.
"It is up to us in 2020," said Pete Buttigieg, the 37-year-old mayor of South Bend, Indiana. "This is our chance to refuse to be taken in by the helplessness."
Biden, popular with blue-collar workers and African Americans, has promised to raise America's standing back to the way it was under Barack Obama, rescuing it from the extreme polarization of Trump's tenure.
But Biden has faced doubts about his health and age -- he is 77 -- as well as the repercussions of the Ukraine affair.
The Democratic elder statesman, who served three decades in the US Senate where he built deep friendships with rival Republicans, bristled at a suggestion he was the candidate seeking to "return" America to normal after Trump.
He referred to Republican attacks on "me, my son, my family," and said: "I have no love." "But the fact is we have to be able to get things done." The centrist Biden is leading polls, trailed by Sanders and Massachusetts Senator Elizabeth Warren who are competing for the party's progressive wing.
Their leftist platform -- universal health care, a tax on the wealthy to reduce inequality, dramatic action on climate change -- is very popular with young and women voters, but makes moderates uneasy.
Buttigieg is in fourth place but has surged to the top in Iowa, which votes first in the Democratic nominating process on February 3.
Further back in the pack are Klobuchar and entrepreneur Andrew Yang, whose staying power continues to surprise.
California billionaire Tom Steyer rounds out the group.
While two women were on stage, Yang, who is Taiwanese American, is the only non-white candidate in the debate. Senator Cory Booker and former cabinet member Julian Castro did not qualify.
Senator Kamala Harris, the only black woman in the race, dropped out earlier this month.
Business Standard has always strived hard to provide up-to-date information and commentary on developments that are of interest to you and have wider political and economic implications for the country and the world. Your encouragement and constant feedback on how to improve our offering have only made our resolve and commitment to these ideals stronger. Even during these difficult times arising out of Covid-19, we continue to remain committed to keeping you informed and updated with credible news, authoritative views and incisive commentary on topical issues of relevance.
We, however, have a request.
As we battle the economic impact of the pandemic, we need your support even more, so that we can continue to offer you more quality content. Our subscription model has seen an encouraging response from many of you, who have subscribed to our online content. More subscription to our online content can only help us achieve the goals of offering you even better and more relevant content. We believe in free, fair and credible journalism. Your support through more subscriptions can help us practise the journalism to which we are committed.
Support quality journalism and subscribe to Business Standard.