Voldemort tries to hang on to his life by killing others and so puts a piece of his spirit in various objects (thereby further reducing himself to an object rather than a person).
Jesus freely lets go of his life and his body is torn apart. Because of his perfect obedience and faith, Jesus swallows up death in victory. And the joke was on death because the means of his death--his torn body--can now be swallowed up by us so that we too may share in his resurrection. And just as Harry was filled with unspeakable dread to realize that he himself was a horcrux, so we ought to be filled with unspeakable joy to realize that we ourselves are the body of Christ, nourished and sustained by Christ who, as head of the body, is the source of our life. Because he is the true death-eater, we can feast on him, the bread of life.
"The last enemy to be destroyed is death." (1 Cor. 15:26)
"When the perishable has been clothed with the imperishable, and the mortal with immortality, then the saying that is written will come true: “Death has been swallowed up in victory.” “Where, O death, is your victory? Where, O death, is your sting?" The sting of death is sin, and the power of sin is the law. But thanks be to God! He gives us the victory through our Lord Jesus Christ." (1 Cor. 15:54-57)