what's meaning of im so beat,why use beat here
are there any other way to say this, or some similar slang?

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The reason the word "beat" is used, is to suggest one is as tired as one who has been beaten up by someone.

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'Beat', when used as an adjective, means "worn-out; fatigued." Therefore, "I'm beat." simply means: "I'm fatigued/exhausted/very tired." 

Another colloquialism would be to say: "I'm spent."

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Beat means bad shape, it is a slang 

For example: I have a beat up car ( my car is in bad shape, it looks ugly) 

I'm so beat means I am in bad shape

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Hello Vivian,

In a certain context it could also mean "lacking anything".
" I am beat for my cash."
" I am beat to my socks." ( lacking everything)

Synonyms (when it means worn out or exhausted) :
" clapped out", " on one's last legs" , "wiped out", "zonked" .

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