"Grow up Donald, grow up, time to be an adult, you're President. Time to do something. Show us what you have," EFE news quoted Biden as saying on Thursday.
Biden had criticised two of Trump's recent messages in which he labelled Senate minority leader of the Democrats Chuck Schumer as 'head clown' and another in which the President-elect criticised President Barack Obama for his 'incendiary comments'.
"It's going to be much clearer what he's (Trump) for and against, and what we're for and against, now that it's going to get down to actually discussing in detail these issues that affect people's lives," Biden said.
The Vice President also said it was 'dangerous' for Trump to be sceptical of US intelligence agencies.
During the campaign and after being elected President, Trump has been using Twitter compulsively for all sorts of purposes, such as insulting opponents and his colleagues, threatening companies or criticising the intelligence community.
New York Republican Representative Chris Collins, a member of Trump's transition executive committee, denounced Biden's response.
"That's a pathetic response," Collins said on Thursday.
"I think it's beneath the office of the vice president. It shows just the angst of the loss of this election by Obama, Hillary Clinton and Joe Biden. Trump is the adult in the room," he added.
This isn't the first time Biden has been outspoken against Trump. Biden in October slammed Trump saying the Republican presidential nominee "lacks any sensibilities about the American people".
"He's not a bad man," Biden said at the time. "But his ignorance is so profound, so profound."