A beautiful term for an extremely Foul smelling fart. The term is made funnier if the fart sounds like quacking duck when expelled from the rectum. Though an SBD can still qualify as a Butt Duck if it is especially foul (emphasis on the word foul/fowl for comic effect). See frequently activated rectal tremble and shit flavored air.
"Fuck Mary, you shit a butt duck! I think you have cancer, something has crawled up your arse and died!"
This is a shameful act that only happens in desperation when you are home alone and have completely run out of toilet paper. With your pants around your ankles, squat walking, and your hands spreading the butt cheeks so you don't smear shit everywhere, you walk this way to your roommates bathroom to finish the job.
Greg had to do the muddy butt duck walk to my bathroom to get more toilet paper.