A guardian angel, played by Keenan Thompson, then guides Baldwin through an alternative reality - a world in which Hillary Clinton had won the 2016 presidential election instead of him.
Virtually everyone in Trump's inner circle - addressing him now as "Mr. Trump," rather than "President Trump" - is depicted as having a better life without him in the White House. This includes Kellyanne Conway, Michael Cohen, Melania Trump and Eric Trump.
At the end of the skit, Baldwin repeats "I want to be president again" until a bell rings and he's brought back to reality. Thompson laments that Baldwin has learned nothing from the experience.
Trump's relationship with SNL has been rocky from the days of his presidential campaign.
He lashed out in 2016 after a skit mocked his performance during a town hall debate. Trump accused SNL of being part of a larger media conspiracy that wanted to prevent him from becoming president. He also directly called out Baldwin.
"Watched Saturday Night Live hit job on me. Time to retire the boring and unfunny show," Trump wrote. "Alec Baldwin portrayal stinks. Media rigging election!"
The president called out Baldwin again this year, writing that his portrayal of Trump was "agony for those who were forced to watch" and a "terrible impersonation."
The Washington Post's Steve Hendrix notes that SNL's spoofing of presidents dates to Gerald Ford. Privately, Ford bemoaned his portrayal on the show by actor Chevy Chase, Hendrix notes. In public, however, Ford laughed along.
In response to Trump's tweet on Sunday, many highlighted his apparent implication that SNL's portrayal of him "can't be legal" and should be tested in courts.
The First Amendment protects freedom of speech, which includes satire and parody.
The White House did not immediately respond to a request for comment.