What is the expression "You beat me"?
About 10 years ago, I heard the expression "You beat me" used in non-literal way; if my perception was correct, they should mean "Your argument or action are too good/outstanding/weird for me to say something further. For instance, I'm having an argument with a friend in order to justify the point or an issue I advocate...All of a sudden, he brings up a so convincing point against my argument that I become "speechless". On this kind of occasion, may I say "hey~ you beat me. You're right in this."?

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Yes, in that way it means, "you've won (the argument)"  or "I have no good response to that."

The feeling is one of friendly surrender and the tone is casual, so I wouldn't ever put it in a larger sentence.  "You beat me" stands alone just fine.  Smile and shrug while you say it. :)

A related phrase meaning "I don't know" is "beats me".

"Do you know where Peachey got to?"  "Beats me."

Answer

Yes. You "beat" someone in a competition. Like a football match or a race.

Other words to describe speechlessness would be
dumbstruck /dumbfound /dumb fold(ed) 
Or you would "have no point".

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