The head has clamping mechanism whose pinching cams are pivotable on planes parallel to one another and to a rotational axis of the head. A clamping mechanism support is mounted in an outer housing (1) of the head in an axially movable manner. The housing and the support are arranged complementarily such that simultaneous relative axial movements of the housing and the support in opposite directions enable the cams to be lifted for allowing positioning, unwinding or withdrawal of flexible cutting wire strands (3), or enable the cams to be lowered for blocking the strands in the head.
