My very wise grandfather used to say "Sarcasm is the sign of a weak person." Audrey is right on.
Obviously, there are different kinds of sarcasm; some if it is hilarious amongst friends. However, the belittling kind - THAT is the wretched kind.
I like the "did that make you feel like a bigger person" response...IME not all the people who deploy the belittling kind of sarcasm realize why they're doing it. It gives them pause in the future.