A saddle with two cutting stations, i.e., front and rear openings, moves forward and backward horizontally within a chassis. The rear opening includes a cutting blade. The chassis includes a front counter blade. A magazine holds a tube bundle and includes a rear face clamp and rear counter blade. In a first cutting operation, skirting at the base of the tube bundle is placed in the front opening and is cut by first moving the saddle rearward against the rear face clamp and rear counter blade, and then frontward against the front counter-blade. In a second cutting operation, the tube bundle is placed in the rear opening. As the saddle is moved frontward, the cutting blade in the rear opening cooperates with the front counter-blade on the chassis to cut the tubes. This second cutting operation is continued until the tubes are cut.