Can a GSXR 750 beat a GSXR 1000?

no

While the above answer is correct for a drag race.. in most cases.. It will always depend on the rider. In a track day race, there are 600s that can beat 1000s. The 1000 will always win on straights though. So the real answer is Yes and No. If your answer was more specific on what kind a race you'd get a better answer. (Edit: YG27)

The question is not clear enough, another key point is the year of the bikes. A newer 750 will smoke a older 1000. However even a gsxr 750 is a lot more bike then most riders can handle of any year.