To accurately cut a work after truing up the side edge to a vice reference line over the total length of the work even if the work is in heavy weight.

The work W is carried on a material sending line to a cutting position CL of a cutter 1 having a cutting tool 7 for cutting the work W. When cutting the work W by truing up the side edge to a work width reference line DL of the material sending line, the tip side of the work W is trued up in the side edge to the work width reference line DL by a vice device 13 of the cutter 1 arranged in the vicinity of the cutting position CL. The rear side of the work W is trued up in the side edge to the work width reference line DL by a work side edge truing-up device 31 in a position passing through by a proper interval to the rear side by the cutting position CL. Even if the work W is carried on the material sending line in a state of obliquely including relative to the work width reference line DL, the work W is surely positioned on the work width reference line DL over the total length, and can be accurately cut.