If the rear diff is removed from a 4wd Mazda gtx will it still drive?

Nope, because the rear c.v's wont have anything to bolt on to.

The only way you could do it (possibly) is to remove the gears from the differential and leave the housing in place to keep the rear axles stable. The differential would still need to be oil filled, and if the gears turn out to be what holds the output axles in place, you're out of luck and this won't work either.