A method for cutting a thin glass including the steps of guiding, by a transport device, the thin glass ribbon over a levitation support, and directing, within a range of the levitation support, a laser beam onto the thin glass ribbon, which heats up the thin glass ribbon at an impingement point of the laser beam. The method also includes the step of blowing, by a cooling jet generator, a cooling fluid onto the track heated by the laser beam so that a region heated by the laser beam is cooled down and a mechanical stress is created. The cooling fluid contains vapor of a liquid at a saturation ratio of at least 0.5 or a plurality of liquid droplets. The liquid droplets form a contact angle on a surface of the thin glass ribbon which is smaller than that of water on the same surface.