A smoothing particle hydrodynamics (SPH) model of quartz glass was established to simulate the ultra-precision cutting process of quartz glass by a mesh-free method for SPH. The material removal mode and strain distribution for the cutting depth of 0.1-1.0 pm were analyzed. The mechanism of crack formation and its influence on the ultra-precision machining process were discussed when the tools of different rake angles were used. The simulated results indicate that quartz glass can be machined in a ductile mode on the micro- and nanoscale. Based on the relation between micro-cracks and plastic strain, the critical cutting depth of brittle-ductile transition is confirmed, and the value is 0.18 pm under given simulated conditions (i.e., rake angle of 0°, cutting speed of 10 m/s and rounded cutting edge radius of 0.1 pm. The negative rake angle cutting tool can obtain a better surface quality, showing that the negative rake angle is more suitable for ultra-precision machining of quartz glass. Furthermore, the experimental results of diamond fly cutting is similar to the simulated results by SPH