A method and apparatus for forming a slide-fastener coupling element from a metal wire having a substantially Y-shaped cross section wherein a blank piece is cut or sliced off from the metal wire by a co-action between a cutoff die and a cutoff punch, and substantially at the same time, the metal wire is chamfered along a next cutting line by a chamfering edge so as to form a substantially V-shaped groove extending in and along the peripheral surface of a head portion of the metal wire and the outside surface of each of two opposed leg portion of the metal wire. The next slicing operation produces a blank piece which is already chamfered at its upper and lower peripheral edges extending along the peripheral surface of the head portion and the outside surfaces of respective leg portions of the blank piece. A finished coupling element shaped from the thus chamfered blank piece is smooth to touch and ensures smooth sliding movement of a slider which will guarantee smooth opening and closing operation of a slide fastener.