The president took to Twitter on Tuesday to deny "fake news" that he had a series of mini-strokes during a mystery visit to hospital in November, saying perhaps they were referring to "another candidate".
Mr Trump Jr wasn't as subtle when calling out Mr Biden's two brain aneurysms and surgeries.
"Yes, Biden had two explosions in his brain, but obviously that has nothing to do with why he can't remember where he is most days," Trump Jr wrote.
Biden suffered two brain aneurysms during his failed bid for the Democratic presidential nomination in 1988, which ultimately went to Michael Dukakis against George HW Bush.
As vice president, he made light of the aneurysms during a 2013 speech where he recounted his doctor's advice on the operating table.
When Mr Biden asked what would happen if he survived the operation, the doctor replied: “Well, the side of the brain that the first aneurysm is on controls your ability to speak.”
“Why in the hell didn’t they tell me this before the '88 campaign?’ It could’ve saved us all a lot of trouble, you know what I mean?” Mr Biden joked.
The physical health and mental fitness of both Mr Trump, 74, and Mr Biden, 77, has been a focus of the 2020 presidential race, and Mr Trump Jr has been a vocal critic of the Democratic nominee throughout the campaign.
A day before making light of Mr Biden's aneurysms, he told Fox News' Mark Levin that he didn't mean to make light of serious health issues.
"The difference is, we're not entrusting the average grandparents with the nuclear football mark. We're not entrusting them with the greatest economy of the world. We're not entrusting them with three hundred and fifty million people now," he said.
"You know, is this guy going to wake up at 3 in the morning to take a phone call? Is this guy going to be capable of doing that? And if we're not sure, should someone other than me be asking this question?"
The neurosurgeon who operated on Mr Biden's aneurysm's, Dr Neal Kassell, told The Washington Examiner in April 2019 that the former vice president appeared to be "totally in the clear".
“Joe Biden of all of the politicians in Washington is the only one that I’m certain has a brain, because I have seen it,” Dr Kassell joked.
Join our new commenting forum
Join thought-provoking conversations, follow other Independent readers and see their replies