No one knows. Katniss just hears about it when they see the dead tributes' faces projected in the sky.
Yoyo_963: It says nothing about his death in the book BUT Suzanne Collins (the author) was working with the director and in the movie he dies by a mutt. In the book he was killed by Clove since later on on Clove recovered the package that Thresh stole
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Thresh's death is never really explained but presumably he is killed byCato. Rue gets caught in a net and then speared by the boy from district 1 (his name is Marvel).
In the book, Cato kills Thresh after he gets his full body armor and is able overpower him.
In the movie, Thresh is killed by the mutts placed in the game by Seneca Crane.
In the book Thresh smashes Clove's temple in with a rock, but in the movie he smashes her against the cornacopia.
He kills Clove because he hears her say to Katniss that they killed Rue, and Thresh killed her for revenge. But he spares Katniss because she helped Rue in the arena.
Peeta
At the Feast Clove attacks Katniss, but before killing her she makes a foment about Rue. Thresh hears her and grabs Clove. Enraged he hits her with a rock and she slowly dies. He doesn't kill Katniss though because she was Rue's ally and feels that he owes her. Being from the Seam Katniss understands perfectly. She feels the same debt to Peeta since he gave her the bread when they were little.
Because Katniss looked after Rue, Thresh's district partner, and she didn't kill her, she even looked after she died and she tells thresh this and he says just this once and runs off.
Clove says "Where's your boyfriend, Lover Boy, District 12? Still hanging on? We'll just let nature take care of him." Then as Clove is about to kill Katniss, Thresh comes up and kills Clove with a rock.