When it comes to crafting perfectly absurd nicknames for political opposition, Donald Trump has got it down to a science. "Crooked" Hillary, "Low Energy" Jeb Bush, "Mini" Mike Bloomberg, "Wild" Bill Clinton, "Lyin'" Ted Cruz, Al Franken-stein, "Cheatin" Barack Obama, Elizabeth "Pocahontas" Warren, "Nervous" Nancy, the list goes on and on. The names are not only employed by him but are co-opted by everyone in his organization, so why they call him "Sleepy" Joe Biden?
Why do they call him "Sleepy" Joe?
A lot of Trump's nicknames seem to play into whatever narrative he's trying to construct in order to discredit his opposition. For Hillary Clinton, it was the imagery of her as a corrupt politician. He constantly played into the collective distrust many people had of the Clintons (and a "liberal agenda" in general) and he'd bring up the email scandal where she had emails hosted on a private server.
Something that both he and members of his administration and White House aides did as well after he took office, although there are some slight differences between the two usage cases.
The name of "Sleepy Joe" comes from Trump's suggestion that Joe Biden is suffering from a cognitive decline of his mental faculties.
Joe has gone on record saying some either off-color or unintelligible things, something that's been attributed to a stutter that he suffers from. Cognitive mental decline isn't uncommon in individuals who are Joe's age, either. The man was born in 1942 and is nearing 78 years of age at this time of writing.
There are reports of Ronald Reagan often asking members of the Secret Service staff at times where he was, but once they reminded him, he'd be "back on track" so to speak.
So "Sleepy" Joe was part of the narrative that Donald Trump and his administration were lining up in their attack of Joe Biden, questioning the mental fortitude of the DNC's top presidential pick and if he would be capable of actually running the country and holding coherent discussions.
President Trump, in the lead up to the election would often say, "Joe Biden doesn't even know he's alive."
It had become an oft-repeated chorus of Trump supporters and the GOP, touting videos and even a faux-trailer called Weekend at Biden's further driving home the narrative that Joe Biden is basically a walking corpse who is running for the highest office of the United States.
Unlike the "Cocaine" Mitch McConnell t-shirt, the Sleepy Joe one wasn't co-opted.
The Senate House Majority leader was accused by Don Blankenship of being a cocaine smuggler (the accusations were tenuously supported, at best) but Mitch, instead of being offended by the moniker, actually used it to his campaign's benefit and managed to raise around $70,000 from selling t-shirts that light-heartedly adopted the nickname.
Joe Biden didn't do the same with the "Sleepy" nickname, however, and the t-shirts that were printed were very much antagonistically designed to depict the former vice president in a negative light.
Other articles of clothing depict some of his more controversial moments, like when Joe Biden said "You ain't black" if you aren't voting Democrat on an episode of The Breakfast Club.
The results of the 2020 election are still pending with President Trump vowing to take the decision to the Supreme Court even if the electoral votes all point in Biden's favor in order to investigate voter fraud.