To supply a sufficient quantity of slurry between a wire and a workpiece to permit efficient cutting by providing a vibration imparting means coming close to a wire row to impart vibration to the wire through a micro clearance.

Driving output from a driving output generating circuit 44 is supplied to magnetic field generators 21, 22. A wire 7 is drawn downward by the magnetic field from the magnetic field generators 21, 22, and the supply of driving output is stopped to return the wire 7 upward by its own elasticity, thereby imparting a specified cycle of vertical vibration to the wire 7. Vertical progressive waves are therefore generated to the wire 7, and more slurry is led in between the wire 7 and the cut part of a workpiece 11 by the progressive waves to carry out efficient cutting. Since the wire 7 and the magnetic field generators 21, 22 never come in contact with each other, the magnetic field generators 21, 22 are not cut or damaged by the wire 7.