Can you just cut the fabric on a prom dress to shorten it?

Probably not just a one-step deal. You have to hem the dress so that you do not have a raw edge at the bottom. You can hire it done for under $20 if need be.

One tip that the tutorials do not mention: do not lay the item on your bed to cut it down. You may end up cutting the bedspread. The dining table or ironing board works nicely.