It was called the Elder Wand, actually.
In order to obtain the Elder Wand, you must take it from its previous owner. This usually involves killing the witch or wizard. Harry does not want this to continue. Therefore, if he rids himself of the wand and dies a natural death, the wand will then be useless.
Furthermore, Harry states that he was happier with his old wand and that the Elder Wand is "more trouble than it's worth."
In the movie, at least they could've had to cut it with Gryffindor's Sword. Or something. It seems like the most powerful wand in the history of everything ever would not be able to have it's magic broken by a simple physical act. It takes magical damage to destroy even normal wands.