If you had a single pure mystery substance and cut it half over and over again until you a bunch really had two other different mystery substances that original substance would have been an

Can't follow this q too well, but from what I think is being asked, your pure mystery substance would be a compound. Sodium chloride would do. Chop and chop and chop (thought experiment) and eventually get down to a sodium atom and a chlorine molecule. Keep temp low, and Cl2 might even not be a gas on the final chops ...