An apparatus is disclosed for cutting a workpiece. A laser beam is directed at successive points along a workpiece surface to be cut and a sensor emits a sensing beam directed at the same successive points as the cutting beam. A beam combining device receives both the sensor beam and the cutting beam and causes downstream beam segments to be collinear with each other as they impinge the workpiece surface. The cutting is thereby able to be carried out in a single pass, and is precise, repeatable and independent of cutting depth, angle of cutting, scoring patterns, material inconsistency, material color, and surface grain variability.