There is disclosed a numerically controlled cutting method of cutting a curved surface SF generated by interconnecting corresponding points mi, ni (i=1, 2, . . . ) on two curved lines CV1, CV2 with a cutter BT of a milling machine having simultaneously controlled five axes or a wire electrode of a wire-cut electric discharge cutting machine. According to the numerically controlled cutting method, curve information specifying the two curved lines CV1, CV2, information on tool radius or wire radius, information on the direction of tool or wire compensation, and division information for dividing the curved lines are supplied as inputs. Using the above items of information an offset position at dividing points mi, ni, which are next to dividing points mi-1, ni-1 at which the cutter BT or wire is currently positioned, is determined. The cutter BT or wire is then moved to the offset position to cut the curved surface SF.