He killed it with Gryffindor's Sword.
Making a horcrux out of a living creature is a dangerous thing, because one only needs to kill the creature to destroy the bit of sealed soul.
In order to destroy a horcrux, its vessel must be put beyond magical repair. For an artifact, that requires some pretty destructive magic, such as fiendfyre, or basilisk venom. But because no magic can ever truly reawaken the dead, anything that can kill a creature can put it 'beyond magical repair.'
And yet, the Sword of Gryffindor, impregnated with basilisk venom, was the instrument used.