Does cutting meat into pieces make it go bad faster?
Yes, as you said, the increased surface area makes it go bad faster.
Not only that, but bacteria on top of the meat can now go to the middle with little resistance.

Consider the expiration date of ground beef and whole beef slabs.

Pork tends to go bad faster than beef, and freshly butchered pig smells of feces (especially right beneath the skin), but they still go bad faster.