Method of manufacturing a tire comprising a tread strip in which blind radial cuts are arranged in the blocks of rubber that form the tread pattern, comprising a step during which the cuts (33) are made in the unvulcanized tread strip (3) intended to cap the green tire. One or more blades (22) are raised to a temperature higher than the vulcanization temperature of the material of which the tread strip (3) is made are caused to penetrate the radially internal face (32) of the tread strip (3) for a sufficient period of time that they superficially vulcanize the walls of the cut in contact with the blade (22) so as to prevent the faces from sticking back together once the blade has been withdrawn from the cut.