Abstract: Algorithm design is presented in the paper for the leather punch and cut with straight and arc cutters, and two kinds of paths and relevant calculation methods are presented according to the cut direction and the contour features. In the first method, the equal deviation approaches are used to find straight cutter position, and in the second method, combined equal deviation and chord length approaches are employed to obtain the positions for the mixed straight and arc cutters. During the cutting calculation process, attention should be paid to searching the cutter library for a proper one and rotating the cutters themselves to prevent from over cutting. The punch paths qualities are optimized by an Improved Greedy-opt2 algorithm. Finally, process samples are given to show the satisfactory results of the algorithm.