Abstract: An auxiliary cutter for precisely cutting through the outer covering of a cable without damaging the inner core is removably attachable to a grinder. An optical cable or electrical cable is fixedly held in a bearing by a fixing ring. A portable grinder is detachably attached to the cutting attachment or the auxiliary cutter to provide a cutting blade. Additional connecting parts enable the auxiliary cutter to rotate 360.degree. relative to the central axis of the cable for cutting entirely the outer surface of the cable being cut. The cutting depth can be adjusted and set by an adjustable screw which fixes the distance between the edge of the cutting blade or wheel of the grinder and the central axis of the cable being cut. A compression spring presses the outer covering of the cable against the grinder cutting blade for cutting the outer covering of the optical cable or electrical cable up to the present cutting depth.