In order to manufacture parts with an outer profile, a workpiece 32 is pressed by a pressure piece 24 through a ring-shaped cutting tool 34. The cutting tool 34 has a plurality of disks with inner cutting edges 62 for removing material from the workpiece 32. The cutting edges are progressively longer in the advance direction, so that each cutting edge removes material chips and the last cutting edge in the advance direction corresponds to the desired outer profile of the part. In order to improve chip removal, the chip chambers 74 located between the cutting edges communicate with the outside through radial connection openings 128 which are distributed all around their circumference. To hold the workpiece 32 securely on the pressure piece 24, a pressure pad 76 extends through the cutting tool 34 and is supported on the side of the workpiece 32 opposite to the pressure piece 32, and a hydraulic piston 80 generates a compression force on the pressure pad 76. To ensure a high dimensional accuracy, a calibrating tool with a passage whose dimensions at the rear outlet side correspond to the set dimensions of the part to be manufactured is arranged behind the cutting tool.