A cutting device includes a mounting head, cutting tools and a bracing element. Each tool has a cutting edge having a recess with a substantially semi-circular contour for accommodating a portion of a workpiece. An engaging protrusion extends into each recess and has a foot circumferential angular range from 20 to 90 degrees. The engaging protrusions project into the recess by ⅕ to 9/10 of its radius. The bracing element extends from one tool and has a surface for supporting the workpiece.