The full form of SU is shut up.
This acronym is most commonly used to represent the phrase “shut up.”

Origin of SU
The first recorded appearance of the phrase this acronym represents appears in 1748. Originally the phrase was written “shut up one’s mouth” but it was shortened to simply “shut up” over many years and frequent usage.

Other Meanings
There are many other phrases that this acronym can represent and it can be used as a standalone term as well. Some of the other phrases that this acronym can represent are “swipe up,” as seen used in Snapchat, “straight up,” “stumble upon,” “student union,” and “socially unacceptable.” As a standalone term, this word can mean a term of endearment for someone close to you, a German or French swear word, another word for nest or vinegar, and a person who does things that are immature and childish.

Conversation Examples
A text message exchange between two friends.

Friend 1: I heard you like Robert Porter.
Friend 2: You did? From who?
Friend 1: I can just tell these things. I am going to tell him tomorrow at school.
Friend 2: SU! No, you are not!