A combination of a cutter and a fastener unit for fastening the cutter to a tool attachment shaft. The cutter includes a cutter body formed therein with a threaded bore. The fastener unit includes a fastener element having one axial end portion provided on its outer peripheral surface with first threads threadedly engageable with a threaded bore in the tool attachment shaft. The other axial end portion of the fastener element is provided on its outer peripheral surface with second threads threadedly engageable with the threaded bore in the cutter body. The first threads are reverse in a direction of helix to the second treads. An end face of the other axial end portion has a size at most equal to an inner diameter of the threaded bore in the cutter body. If the fastener unit includes a clamper in addition to the fastener element, the cutter body is formed therein with a through bore in place of the threaded bore, and the clamper is received in the through bore. The clamper is formed therein with a threaded bore with which the threads on the one axial end portion of the fastener element is engageable.