Why does bree tanner die?

Answer 1

Because, according to the Volturi, she broke the one of the most important vampire laws: not to expose themselves (vampires), especially by drawing attention to themselves by doing reckless things such as killing many people and using their powers out in the public eye. Bree Tanner did two of these things: drawing attention and excess killings. Although, she was a newborn and was not taught properly and not told of such things. Therefore, her execution by the Volturi, in a sense, was a bit extreme for the situation.

Answer 2

Bree Tanner dies because she is killed by the Volturi at the end of the battle in the "Eclipse" novella. She is considered a threat by the Volturi and is executed to prevent any risk of her revealing information about the vampire world.