PURPOSE: To connect the connected parts of cut loci of line segment data extended over two frames positively to each other.

CONSTITUTION: Long cutting data is divided into plural frames, and a cutting sheet is cut frame by frame on the basis of cutting data. Connecting cut processing based on connecting process data for connecting the connected parts of the cut loci 60a, 62a of line segments 60, 62 extended over two frames is applied to these connected parts. As an example of this connecting cut processing, a cut locus 54a or 56a of polygonal, circular, cross shape, or the like is formed at the connected parts of two cut lines. In the cutting based on the cutting data frame by frame, the connecting process data of a preceding frame is vector-sorted together with the cutting data of the following frame, and the connecting cut processing of connecting process form is applied efficiently to the connected parts.