“Stick a fork in him (he’s done)”

“Stick a fork in him” means “he’s done.” It’s a barbecue term; the piece of meat is cooked and you can stick a fork in it and take it off the grill.
 
The term is used in sports, often in baseball. You can “stick a fork” in the starting pitcher and bring on the relief pitcher. The term is first recorded from baseball pitcher and announcer Dizzy Dean. Dean was born in Arkansas, but the “stick a fork” phrase traveled well into Texas.
 
   
Wikipedia: Dizzy Dean
Jay Hanna “Dizzy” Dean (January 16, 1910–July 17, 1974) was an American pitcher in Major League Baseball, elected to the Baseball Hall of Fame. He was born in Lucas, Arkansas, and was a life long resident of Wiggins, Mississippi. He was a pitcher for the St. Louis Cardinals (1930–1937), the Chicago Cubs (1938–1941), and briefly for the St. Louis Browns (1947).
 
25 July 1944, Berkshire Evening Eagle (Pittsfield, Massachusetts), pg. 5, col. 2 (Sports Roundup by Fritz Howell of the AP in New York—ed.):
Today’s Jest Star
John P. Carmichael, Chicago Daily News: Dizzy Dean as a broadcaster is tickling his listeners’ ribs with this one: When a pitcher starts going haywire, either through wildness or throwing base hits, Dean chirps over the mike: “You can stick a fork in him folks—he’s done.”
 
16 June 1950, Waterloo (Iowa) Daily Courier, pg. 13, col. 1:
One of Leo Durocher’s famed remarks when removing a pitcher is supposed to be “Stick a fork in him; he’s done!”
 
3 March 1953, New York Herald Tribune, Red Smith’s Views of Sport, pg. 27, col. 2:
They Stuck a Fork in Bobo
(...)
It was the adequate torso of Mr. Bobo Newsom, a professional pitcher, aged forty-five going on forty-six, who has been one of the scenic glories of organized baseball since the Battle of San Juan Hill.  Mr. Newsom looked superlatively fit. He confessed that he had trained faithfully all winter serving as a tourist attraction in Winter Park, Fla., flapping flapjacks in the window of a short-order house.
 
“Do you mean to say,” Mr. (Athletics coach James J.—ed.) Dykes was asked incredulously, “that he is one of your pitchers?  Pardon my ignorance, but not even Rand-McNally could trace him around.”
 
“You should see him throw,” the manager said. “He worked two games for us against the Senators last year after we got him from Washington. He won one, when I had to take him out in the ninth.  In the other, he ran from first to third in the eighth inning and he was winded. He lost his control and I said, ‘Stick a fork in him, he’s done.’  So I relieved him and we finally lost in the eleventh.”