Dorothy Parker is mid-20th century writer famous for her incisive wit ("Beauty is only skin deep, but ugly goes clean to the bone"). This song though, has nothing to do with her - that Prince put her in the title of this surreally jazzy song is pure coincidence.
Prince's saxophonist on Sign O' The Times, Eric Leeds, recalled to Mojo: "When I first heard it. I thought, Wow, of all people to even know who Dorothy Parker was! I kinda thought maybe [girlfriend, backing singer] Susanna or [Revolution guitarist] Wendy Melvoin had told him about her. But it turned out he didn't have any clue; he just picked the name because of how it sounded, and only after the fact did they tell him to she was."
The song tells a story about a waitress with a sharp tongue, who mocks our hero when he orders a fruit cocktail ("Sounds like a real man to me"). They end up taking a bath, but he leaves his pants on, since he kinda has a girlfriend. When the phone rings, he knows that his time is up, but he looks forward to doing it again.
As we said, the song is quite surreal. If indeed Prince had no knowledge of the writer Dorothy Parker, it certainly is serendipitous that he armed his character with clever quips, just like the real Parker.
This is one of many songs with a Joni Mitchell reference. The line, "And it was Joni singing, 'Help me I think I'm falling,' relates to Mitchell's 1974 track "Help Me."
Mitchell's influence also shows up on the Prince track "When We're Dancing Close And Slow" - the title is a line in her song "Coyote."