To make it possible to eliminate a protection film for protecting the surface of a product part W' and to surely prevent the damage of the surface of the product part W'.

By simultaneously supporting the underside of a workpiece W with a work table 5 and both conveying belts 4, 4' and holding both sides of the workpiece W by a holding means 8, they are moved in the X-direction at the same speed and also a machining head 3 is moved in the Y-direction while emitting a laser beam from the machining head 3 onto the workpiece W. In this way, the product part W' having the required shape is cut down from the workpiece W. The cut product part W' is placed on the conveying belts 4, 4' and, after that, the work table 5 and the holding means 8 holding the surplus material of the workpiece W are elevated by an elevating means 7. Only the product part W' is supported on the conveying belts 4, 4' and, after that, the product part W' is discharged to the carry-out position C with the conveying belts 4, 4'.