I believe that the Spanish had at least one stone mortar in Florida. I can't imagine why they would go to the trouble of making round stones for it.
Because labor was cheap and iron expensive.
I figured that someone would go out and collect the size stone needed and not worry too much about the shape.
Large bore stone mortars fired a natural version of grape shot in a high arc. These stones would have been used as found, and they were probably around the size of a fist. The stones were placed in a woven basket, and the basket lowered down the bore. The U.S. even had a couple made; one bronze 16-inch M1839 stone mortar survives at West Point.
If the 2.75-inch stone ball is indeed carved stone shot, then in all probability it was made to be fired from a 'cannon'.