It's informal and colloquial, but in the U.S. it is correct. There is a completely different word "deadbeat," which can mean "a person who doesn't pay his debts," but the two uses would never be confused.
Here are various ways of saying the same thing. Standard: "I'm exhausted." Informal and colloquial: "I'm beat." "I'm dead on my feet." "I'm dead tired." "I'm pooped." "I've had it." "I'm all in."
After reading Brian and Matt, I did a search just to make sure I wasn't wrong, but I'm not. I was able to find many examples of use:
"Can't this wait until tomorrow?" Scott asked in a hoarse voice. "I'm dead beat."--U.S. novel, 2009
"I'm sorry, girls, but I'm dead beat. And you don't want a dead body on your hands at this late hour, now, do you?” U.S., 2013
""Yes," I reiterated, "I'm going home, but not on this train. I'm dead beat."--Loren Eiseley, U.S., 1975
"Take the saddle off my horse and put 'er up," groaned Shorty. "I'm dead beat!"--Max Brand, U.S., 1922
“I’ll tell all that later,” I said. “I’m dead beat. I’m a rag.” --H.G. Wells, "The First Men in the Moon," confirming this was also Victorian British usage.