Silver yes, copper, not so much.... but your coin is broken and not cut. If you dug it in a farm field it likely got caught in the equipment. and the other half is there somewhere.
Coppers are awesome... Nice finds! I also have one that has exactly 1/4 cut from it, and another with a bunch of holes. Guess the early settlers used them for a bit of everything. Kind of reminds me of the time I pulled an intake manifold from my truck and found someone used two nickels and a craftsman socket to plug the EGR port. LOL