Why not?
If it's alive it's a sheep. If it's dead it's mutton. (i.e. saying that something is 'mutton' must mean that it's dead; you can't have live mutton!)
OK, I suppose you could say 'As dead as beef' (which, for similar reasons, would mean the same thing) but the phrase originates in times when the meat found in most households would have been mutton. (Indeed, apart from the very rich, few people probably tasted any other sort of meat).
BTW: Mutton, properly cooked, tastes vastly better than lamb; it's simply not fashionable to eat it.