Re-capitate? There really is no "opposite" of a word that means to remove a head, since you can't very well put it back on.
Its was the Guillotine also known as Madam La Guillotine. This was used in France. In other areas of the world a Sword or Axe where used.
To decapitate is to remove the head.
should i kill you or decapitate you with the knife
Depends on the size, mass, velocity and placement of the projectile.