So if you mean a student is cheating, for example, on a test / exam:
Catch is my preferred verb here. "I caught him cheating on the test"
(In your headline you use "catch up" - this is a phrasal verb meaning "get up to date" or "become level with in a competition"
"Pick" doesn't work for me. It means many things, but normally it means "choose"
"Pick up" means to collect from the floor eg, "Please pick up your dirty clothes". "Pick up on" can mean "ldentify" or "notice" or "give attention to".
"I want to pick up on the points you were making" (attention to)
"I picked up on his bad attitude" (notice / identify)