To make a mistake, to go wrong.
You really fucked up this time.
To botch or make a mess of.
I fucked up question 3 of the exam.
To injure or damage badly.
I fucked up my knee while running the marathon.
To cause someone to make a big mistake.
(used only in imperative) Short for shut up.
Fuck up, mate! I don't want to listen to you!