Machine for punching holes through a longitudinal sheet or wheel rim passing in a horizontal direction, using punches, and also for cutting said sheet to obtain sheet portions or pieces. The machine is characterized in that the punching and cutting operations are performed by a single power unit, such as an oleohydraulic cylinder (2) secured to a frame and positioned at the top in a vertical direction. The shaft of said cylinder is connected to a cutter-holding carriage (4) which, as it moves downwards to cut the sheet (10), brings with it an upper support means (19) that forms part of a punching device (6), the punches of which are guided on a lower front carriage (8) that also forms part of the punching device (6).