The invention relates to a laser cutting method for cutting a stainless steel workpiece using laser beam generation means comprising a silica fiber with an ytterbium-doped core to generate the laser beam. Preferably, the laser beam generated by the ytterbium-based fiber has a wavelength between 1.07 and 1.09 μm, a quality factor of the laser beam is between 0.33 and 8 mm·mrad, and the laser beam has a power of between 0.1 and 25 kW. The assistance gas for the laser beam is chosen from nitrogen, helium, argon and mixtures thereof, and, optionally, it further contains one or more additional compounds chosen from O2, CO2, H2 and CH4.