That's got me beat.
What does this mean exactly?

Question

Answer

I agree with Nanren888. 'It's got me beat' or 'you got me beat' is an idiom used to mean 'I don't know the answer; I cannot figure it out.' 
A: 'What is the most populous country?' B: 'You got me beat = That's got me beat' 

I't beats me' is another informal expression that you can use when you cannot understand something. It is often used with a 'question word': 
'It beats me (= I don’t know) why he did it.' 
'What beats me is how it was done so quickly' (= I don’t understand how).

Answer

That is too difficult for me to answer.
or
That is too difficult for me to understand.

What is capital city of Korea?
That's got me beat.

For other dialects, you might look up "beaten" instead of "beat".

Answer

It means :  정망 몰라
        "I have no idea"  
         I'm thinking very hard but I can't think of the answer to your question.

You can also say "You've got me stumped" or "I'm stumped"  which means the same thing.