From Steely Dan fame.
According to a Steve Martin film, in Haiti if you say “I divorce you” three times you are divorced. I, for one, will not argue with such an authority as “The Man With Two Brains.”
I doubt that the foregoing has anything to do with the song, though.
Papa say Ohhhhh. No hesitation. No tears and no hearts breaking-no remorse.
A great tune!
Yes it is! 
And who’s Papa? Doc Duvalier?
I’d always presumed that the Papa in the song was either Babs or Clean Willie’s Dad-disapproving of their cavalier attitude towards matrimony, and Babs carrying on with “the Charlie with the lotion and the kinky hair” shortly before the “dolly back, now we fade to black” 
This bit from Steve Martin’s “Wild and Crazy Guy” album is the first thing I thought of when I saw this thread title:
[wild and crazy guy voice]You say “I break with thee, I break with thee, I break with thee…then you throw dog poop on her shoes”[/wild and crazy guy voice]
In the song’s storyline it’s a divorce triggered by the wife’s trip to Haiti. In particular the unmistakable evidence she’s been unfaithful, a black baby.
I don’t think the phrase has any particular meaning outside the song.