At an event for black and Hispanic journalists, the presumptive Democratic presidential nominee compared the question to asking CBS News correspondent Errol Barnett if he was using cocaine during the interview.
"No, I haven't taken a test. Why the hell would I take a test?" Come on, man. That's like saying you, before you got on this program, you take a test where you're taking cocaine or not. What do you think? Huh? Are you a junkie?," Mr Biden said.
When asked for a response to Donald Trump, who has bragged about passing a cognitive test and made Mr Biden's mental state an issue for voters, the former vice president dismissed the question as trying to provoke a reaction.
"Well, if he can't figure out the difference between an elephant and a lion, I don't know what the hell he's talking about. Did you watch that -- look, come on, man," he said, in reference to Mr Trump's cognitive test discussed during an interview with Fox News.
"I know you're trying to goad me, but I mean . . . I'm so forward-looking to have an opportunity to sit with the President or stand with the President and the debates."
While the Biden campaign did not respond to CBS's request for additional context comparing a cognitive test to a test for cocaine, they told Politico that Mr Biden gave a deserving response to a preposterous question.
"It was a preposterous question deserving of a response that showed the absurdity of it all," a Biden official told Politico.
Mr Trump, 74, has challenged Mr Biden, 77, to take the Montreal Cognitive Assessment, used to test dementia, as the question of cognitive decline has become a focus for both candidates in the 2020 election.
At a campaign event in June, Mr Biden previously said he's "been tested and I'm constantly tested" when asked about his mental state, but the CBS News interview released on Wednesday is his first confirmation that he has not taken a formal test.
"I can hardly wait to compare my cognitive capability to the cognitive capability of the man I'm running against," Mr Biden said in June.
The Trump campaign has mocked Mr Biden's verbal gaffes as part of its digital focus, making a 401 error page an image of Mr Biden saying "you are as lost as me", hosting videos on the Barely There Biden website, and launching a faux investigative series titled "Truth over Facts" in reference to a comment made by Mr Biden in 2019.