An apparatus for making a fracture cut between the cup and the safety ring in plastic caps, which comprises rotary elements provided with at least one mandrel that can be arranged inside the cup and is suitable to produce the rolling, about its own axis of symmetry, of the side wall of the cup along the cutting edge of a blade for making the cut, the blade being associated with an inlet path portion adapted to axially offset the cup with respect to the rotation axis of the mandrel by clamping the side wall against the mandrel; the apparatus also comprises elements for recentering the cup with respect to the rotation axis.