Mr Trump shared a tweet mocking the ex-vice president for wearing a mask during a Memorial Day ceremony event while Trump went without one.
"An absolute fool to talk that way. I mean every leading doc in the world is saying we should wear a mask when you're in a crowd," Mr Biden said during a socially distanced interview with CNN.
"This macho stuff, for a guy -- I shouldn't get going, but it just, it costs people's lives. It's costing people's lives," Mr Biden said. Trump's position amounts to "stoking deaths," he said.
He added: "Presidents are supposed to lead, not engage in folly and be falsely masculine."
Joe Biden: President Trump is "an absolute fool" to mock wearing face masks.
He added: "Presidents are supposed to lead, not engage in folly and be falsely masculine" https://t.co/RI5zjN15Jf pic.twitter.com/2VrHaKwVFV— CNN Politics (@CNNPolitics)May 26, 2020
Mr Biden's comments came as Mr Trump denied mocking his presumptive presidential opponent's mask-wearing, while at the same time calling out a reporter for wearing a mask during a Rose Garden event.
"You want to be politically correct," the president said to Reuters reporter Jeff Mason, whom he had asked to remove his mask to ask a question more audibly amid the coronavirus outbreak.
Mr Biden and wife Jill Biden wore black masks on Monday to a Memorial Day event in Delaware, while the president and wife Melania Trump did not for ceremonies in Baltimore, Maryland and Arlington, Virginia.
The president shared a tweet from Fox News host Brit Hume on Monday night that made a joke of Mr Biden's mask-wearing.
"I thought that was fine," Mr Trump said. "I wasn't criticising him."
During the interview with CNN on Tuesday, Mr Biden said wearing a mask projected leadership, not weakness.
He said he feared that the president – whose supporters gleefully seize on Mr Biden's gaffes – was himself "missing a step", adding that he thought Mr Trump was "someone who's struggling to control his emotions" and who becomes "more erratic the more he feels behind the curve".
In recent weeks Mr Trump has claimed there was a conspiracy by the previous administration to sabotage his presidency, that there is widespread fraud in mail-in voting, and that a TV presenter may be guilty of murdering a young woman who died of natural causes.