1. Cut the bread into three.
2. Cut the bread into three pieces.
Are both sentences correct?
They both sound unnatural to me, though grammatical.
As the others have said, it's unusual to cut a large loaf into just three pieces but if that's what you want the listener to do, then that's what you should say. However, to avoid any confusion, I would say "Cut the loaf into three". You'll also need to make it clear if you want the three pieces to be of equal size.I mean a big loaf of bread to be cut into pieces.