A saying used to say that something is meant to be deep but epically failed. A paper cut is typically the most minor of the cuts--barely breaking the skin, so for something to be "deep like a paper cut" means that it is hardly deep at all.
Jessica: Look, I know that you like using men like tissues, but you are thirty-freaking-three now. I really think you ought to settle down. Find a man who can tame you.

Emily: Maybe some women aren't meant to be tamed. Maybe they just need to run free until they find someone just as wild to run free with them.

Jessica: Wooow. Quoting Sex and The City. Deep like a paper cut.
by hahahehehahahohahahehehahaho December 30, 2011
Get the Deep Like A Paper Cut mug.