A numerically controlled groove-stamping machine which includes an indexing unit rotatable stepwise by means of a positioning drive about a rotational axis as a function of a stroke of a punch of the groove-stamping machine. The indexing unit is adapted to be driven, in a stepwise fashion, in two intersecting directions running at right angles to the rotational axis. A numerically controlled automatic multiple tool set is provided with the set being equipped with, for example, a stator groove and cut-off tool, a rotor groove tool, and vent hole tools. The tools of the multiple tool set, in accordance with the work steps to be executed, are adapted to be brought into engagement in an individually controllable manner.