When someone makes a cheeky, sassy or smart-alecky remark, they are often accused of being "cute." Technically speaking, it means making a joking response to a serious situation.
For example, a shopper is looking through the various turkeys in the large freezer at the supermarket. Not finding one large enough, she asks a store employee:
"Excuse me, sir, but do these turkeys get any larger?"
"No, m'am, they're all dead."
She might then indignantly respond, "Don't get cute with me!"