An apparatus and a method for cutting a cap are described, with a cutting device comprising a first blade for making a first circumferential cut, a second blade for making a second circumferential cut at an axial distance from the first circumferential cut, and one or more vertical and/or oblique blades for making one or more vertical and/or oblique cuts arranged between the first and the second circumferential cut, with a spindle comprising an engaging portion having one or more circumferential abutting surfaces arranged to contact a lateral wall of said cap, and a circumferential receiving hollow portion receiving at least partially and without contact the first blade, the second blade and the one or more vertical and/or oblique blades.