Cutting device to form on a capsule for closing a container at least one connecting strap that keeps the capsule attached to the container after opening, the cutting, device comprising at least one cutting edge to make at least one cut on the capsule, the at least one cutting edge comprising a cutting start capsule inlet, a cutting end capsule outlet, and at least one transition cutting portion arranged on the capsule inlet and/or on the capsule outlet to form at least one cusp-shaped end zone, the at least one cutting portion being retracted with respect to a remaining part of the at least one cutting, edge so as to penetrate less the capsule of a remaining part of the at least one cutting edge reducing stress concentration and preventing initiation of a fracture in the at least one cusp-shaped end zone.