A workpiece is machined by a primary cutter such as on a lathe, in a primary machining mode, and then any workpiece portions left uncut by the primary cutter are machined by a compensation cutter in a compensation machining mode to thereby produce the desired final cut shape. To effect this cutting operation, data on the shape of the workpiece, the desired final cut shape, and the shape of the primary cutter are entered into an NC apparatus, and the uncut workpiece portions are computed based on data entered in the NC apparatus. A compensation cutter suitable for cutting off the computed uncut workpiece portions in the compensation machining mode is selected from a plurality of cutters, and data on the depth of cut and the clearance of the compensation cutter are set into the NC apparatus. Paths of travel of the compensation cutter as determined from the uncut workpiece portions, the depth of cut of the compensation cutter, and the clearance of the compensation cutter are computed in the NC apparatus. The uncut workpiece portions are then cut by the compensation cutter.