[Task] A sheet material is cut in a predetermined closed loop shape.[Means for solving task]A cutting apparatus for a sheet material, comprises: an air table which is capable of ejecting or sucking air through a plurality of minute punching sections thereof; a template having at least one recess groove section in a predetermined closed loop shape mounted and fixed onto the air table and a punching section located at each of positions on the template which is coincident with a position of each of the punching sections of the air table; a cutter blade disposed on an upper position of the sheet material mounted on the template to cut the sheet material along the recess groove section of the template; and cutter blade driving means which is capable of moving and rotating the cutter blade in X, Y, and Z coordinate axes.