The origin of the phrase probably comes from either horse selling, or horse betting, and was usually seen as a hush-hush way of doing some possibly illegal dealing. Over time, it has passed into common parlance a a euphimism for visitng the toilet - one of many similar expressions - my dad always used to say he was going to turn his bike round (!)
when i was a kid,my dad would get ready to go out friday night.i would ask him where you going dad! ive got to see a man about a dog he replied.but of course he was going to the pub!!i wonder if its the same sought of thing??
The expression comes from the long forgotten 1866 play Flying Scud by a prolific Irish-born playwright of the period named Dion Boucicault. One of the characters uses the words as an excuse to get away from a tricky situation. This character, an eccentric and superannuated old jockey, says: "Excuse me Mr. Quail, I can't stop; I've got to see a man about a dog". This is the only thing that seems to have survived from the play.