Does cutting meat into pieces make it go bad faster? Assuming I buy some chicken thighs, and it would be fine in the fridge for a few days until I'm ready to cook it, if I cut the thighs into pieces and mix with some veggies put into a separate container from the cut-up veggies (thanks @Joe), would the raw stir-fry mix (in a tupperware in the fridge) keep the same amount of time? Or would the increased surface area make it go bad faster? Does the answer change if it's beef or pork?
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.