The cutter has a conical main body (1) rotatable along an axis and having a groove (6) formed along a generatrix of the cone. A spacer (8) is removably attached with an engagement area extending to the generatrix between one (6a) of the two opposite side faces (6a,6b) of the groove and one side face of the slide member (7), which has a cutter blade and slides on the groove. Another side face (7a) of the slide member has a complementary engagement area. A plate (22) is mounted between another side face of the slide member and another side face of the groove and is pressed towards the one side face of the groove whilst the other side face of the slide member has a protruding area (21) with a V-shaped cross-section. A side face of the plate has an indent area (24) with V-shaped cross- section so that the protruding area comes into close contact with same.
