The head (9) of the cutting apparatus (4) of the laser comprises a gas supply through a device such as a barrel dispenser which chops the blowing flow rate, which produces a better discharge of the liquid slag melt by the laser beam (16, 18) out of the plate (19) to be cut. A measurement (36) of backscattered light is made in order to check the good quality of cutting, the amount measured being smaller if the cutting actually passes through the plate (19), and the frequency or the pressure of the blowing pulses is adjusted by a controlling device (39) to keep the measure to a minimum by optimizing the slag discharge conditions.