A machine tool for cutting workpieces includes a cutting head with at least two cutting units each providing cutting beams directed at the workpiece so as to impinge thereon closely adjacent each other to cooperate in the cutting action. The machine tool includes a worktable to support the workpiece, and the workpiece and cutting head are relatively movable to provide a cutting line in the workpiece. At least one of the cutting units is movable relative to the other so that the angular relationship of the cutting beams may be varied, and the supply of the cutting medium is separately controlled for the cutting units. In one embodiment the cutting beams are high speed water jets which may contain abrasive and the cutting characteristics of the jets may be varied.