To prevent slurry adhered to a wafer from being dried after completion of a cutting process, and thereafter easily and quickly clean-remove the slurry adhered to the wafer in the later washing process.

While rows 17 of wires tensed in parallel, are allowed to travel by a wire traveling mechanism, a work 25 is cut by feeding slurry 23 containing free abrasive grains to the rows 17 of wires by a slurry feeding mechanism 19, and by feeding-moving the work 25 in the direction in which the work is brought into contact with the rows 17 of wires by a feed mechanism. When the cutting process of the work 25 is completed, the feed and movement of the work 25 by means of the feed mechanism is stopped, and the running action of the rows 17 of wires by means of the wire traveling mechanism, and the feeding operation of the slurry 23 by means of the slurry feeding mechanism 19 are controlled to be proceeded.