Apparatus for cutting capsules, wherein each capsule comprises a closure portion for closing a container and a skirt portion for surrounding a neck of the container, said apparatus comprising: - a carousel rotatable around a carousel axis; - two or more transport units carried by said carousel, each transport unit being configured to transport a capsule along a path defined by a rotation of said carousel, each transport unit comprising a base and a locking member arranged above said base, said base being rotatable about a lower axis and being configured to receive the capsule with the closure portion facing towards said base, said locking member being rotatable around an upper axis coaxial with said lower axis and being configured for insertion into the capsule inside the skirt portion so that the closure portion of the capsule can be retained between said locking member and said base; - a cutting device arranged along said path for cutting the skirt portion of a capsule which is transported by the respective transport unit and which rolls on said cutting device; - for each transport unit, an abutment carried by said carousel and arranged around the upper axis of the respective locking member, said abutment being movable in a radial direction, where "radial" refers to said carousel axis, with the possibility of assuming an abutment position, in which the abutment can press the skirt portion of the capsule against said cutting device while the capsule rolls on said cutting device and the skirt portion is cut, and an insertion position, in which the abutment can be inserted into the skirt portion of the capsule before the skirt portion is cut; characterized in that, for each transport unit, the respective abutment is rotatable around a respective abutment axis that is movable in said radial direction with respect to the respective upper axis, wherein the abutment axis is offset with respect to the upper axis when the abutment is in said abutment position. - a carousel rotatable around a carousel axis; - two or more transport units carried by said carousel, each transport unit being configured to transport a capsule along a path defined by a rotation of said carousel, each transport unit comprising a base and a locking member arranged above said base, said base being rotatable about a lower axis and being configured to receive the capsule with the closure portion facing towards said base, said locking member being rotatable around an upper axis coaxial with said lower axis and being configured for insertion into the capsule inside the skirt portion so that the closure portion of the capsule can be retained between said locking member and said base; - a cutting device arranged along said path for cutting the skirt portion of a capsule which is transported by the respective transport unit and which rolls on said cutting device; - for each transport unit, an abutment carried by said carousel and arranged around the upper axis of the respective locking member, said abutment being movable in a radial direction, where "radial" refers to said carousel axis, with the possibility of assuming an abutment position, in which the abutment can press the skirt portion of the capsule against said cutting device while the capsule rolls on said cutting device and the skirt portion is cut, and an insertion position, in which the abutment can be inserted into the skirt portion of the capsule before the skirt portion is cut;