We report on quartz and glass cutting by a lateral scanning of femtosecond pulses (150 fs at 1 kHz repetition rate) of 800 nm wavelength at room and low pressure (5 Torr) air ambience. Pulses were focused by a low numerical aperture (NA0.1) objective lens. Optimization of fabrication conditions: pulse energy and scanning speed were carried out to achieve large-scale (millimeter-to-centimeter) cutting free of microcracks of submicron dimensions along the edges and walls of the cut. Cutting through out the samples of 0.1-0.5 mm thickness was successfully achieved without apparent heat affected zone. At low air pressure (5 Torr) ambience, redeposition of ablated material was considerably reduced. It is demonstrated that the damage on the rear surface was induced by the stress waves, which originated from the plasma ablation pressure pulse. The mechanism of femtosecond-laser cutting of transparent materials at high irradiance and the influence of stress waves generated by plasma plume are discussed.