The device comprises a cast-off shaft from a smooth trailing end of which tapped workpieces are discharged. A thread cutter at a leading end of the cast-off shaft cuts an internal thread in a workpiece blank to form a tapped workpiece. The tapped workpieces passes in succession over the thread cutter and along the cast-off shaft. The cast-off shaft is an offset shaft having a straight upstream portion formed with the leading end and coaxial with the thread cutter.A straight intermediate portion is disaligned from the upstream portion and includes an obtuse angle with the upstream portion. A straight downstream portion is disaligned from the intermediate portion and includes an obtuse angle with the intermediate portion and parallel to the upstream portion. A thread is cut and held against rotation to effect cutting of the respective thread and cause the respective workpiece to advance axially on the thread cutter and pass to the trailing end of the cast-off shaft by shifting of preceding workpieces along the shaft by workpieces following from the thread cutter
