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.