Abstract: A die-head of a cutting machine comprising a pair of relatively rotatable annular plates which movably hold cutting tools therebetween, a tool retracting lever with a stop, pivotally connected to one of the annular plates, a slide integrally connected to the other annular plate and peripherally pressed by a spring, and a pivotable cam plate with a projection bearing against the stop, the slide having a groove into which is engaged the projection of the cam plate, whereby the displacement of the lever, resulting from the movement of a workpiece causes the cam plate to rotate, thus resulting in a rotation of the slide to automatically retract the cutting tools.