A rotary cutting head uses flexible strands of cutting wire that can be placed inside said cutting head. The clamping mechanism of the cutting head comprises pinching cams that are mounted in such a way as to be pivotable on planes that are parallel to one another and to the axis of rotation of the cutting head. The support for the clamping mechanism is mounted in such a way as to be axially movable in the outer housing of the cutting head. The outer housing and the support are complementary to each other such that simultaneously applying a relative axial movement to the outer housing and the support in opposite directions enables the pinching cams to be lifted, allowing the cutting strands to be placed, unwound, or retracted, or enables the cams to be lowered in order for the cutting strands to be blocked within the cutting head.
