A laser machining apparatus comprising: a machining apparatus main body including a table on which a plurality of skids are arranged, and configured to irradiate a material mounted on the skids with a laser beam from a laser head and cut the material; and a control device configured to control the machining apparatus main body to cut around an opening forming region (51 - 64) set in the material and form an opening, wherein the control device determines that the opening forming region where a scrap rising after processing is to be formed in a plurality of scraps formed by cutting around the opening forming region is a first opening forming region, determines, in a case where the first opening forming region is processed and the scrap rises, whether or not the opening forming region is an opening forming region where the scrap rising reaches and interferes with the laser head and adds a predetermined interference width to an outer circumference of the opening forming region (55, 56) where it is determined that the scrap rising interferes with the laser head, determines that the opening forming region where the laser head is moved to a position at which the laser head interferes with the scrap rising is a second opening forming region (57 - 60, 61 - 64), and controls the machining apparatus main body to perform processing in such a processing order that the second opening forming region is processed prior to the processing of the first opening forming region in a case where the scrap of the opening forming region (57-60, 61-64) interfering with the interference width added region (55a,56a) is determined not to rise, and controls the machining apparatus main body to form a joint in the opening forming region and determines a processing order of all opening forming regions in a case where the scrap of the opening forming region interfering with the interference width added region is determined to rise, and starts the processing from a region with the shortest moving distance of the laser head in order of proximity in cases where it is determined that there is no opening forming region where the scrap generated after processing is to rise, or that there is no opening forming region where the scrap rising reaches and interferes with the laser head, or that there is no opening forming region interfering with the interference width added region. a machining apparatus main body including a table on which a plurality of skids are arranged, and configured to irradiate a material mounted on the skids with a laser beam from a laser head and cut the material; and a control device configured to control the machining apparatus main body to cut around an opening forming region (51 - 64) set in the material and form an opening, wherein the control device determines that the opening forming region where a scrap rising after processing is to be formed in a plurality of scraps formed by cutting around the opening forming region is a first opening forming region, determines, in a case where the first opening forming region is processed and the scrap rises, whether or not the opening forming region is an opening forming region where the scrap rising reaches and interferes with the laser head and adds a predetermined interference width to an outer circumference of the opening forming region (55, 56) where it is determined that the scrap rising interferes with the laser head, determines that the opening forming region where the laser head is moved to a position at which the laser head interferes with the scrap rising is a second opening forming region (57 - 60, 61 - 64), and controls the machining apparatus main body to perform processing in such a processing order that the second opening forming region is processed prior to the processing of the first opening forming region in a case where the scrap of the opening forming region (57-60, 61-64) interfering with the interference width added region (55a,56a) is determined not to rise, and controls the machining apparatus main body to form a joint in the opening forming region and determines a processing order of all opening forming regions in a case where the scrap of the opening forming region interfering with the interference width added region is determined to rise, and starts the processing from a region with the shortest moving distance of the laser head in order of proximity in cases where it is determined that there is no opening forming region where the scrap generated after processing is to rise, or that there is no opening forming region where the scrap rising reaches and interferes with the laser head, or that there is no opening forming region interfering with the interference width added region.