The Severing Crime Edge

Killing Goods are murder weapons handed down from generation to generation within the families of their owners. They are cursed to compel their current owners to repeat the original murders. The curse also makes them indestructible. Kiri Haimura is the current owner of a pair of shears that can cut seemingly anything, although the only thing he wants to cut is hair. One day he meets Iwai Mushanokoji, a girl of whom he has only heard rumors that her hair cannot be cut, a girl who can grant one wish, any wish, but only to the person who murders her. Every morning he cuts her hair, which grows back every night; and every day he helps protect her from people who know about her curse and who want a wish granted.

Synopsis from Anime News Network