Soda–lime glass has a wide range of applications in the fields of smart electronics, optical components, and precision originals. In order to investigate the effect of processing parameters on picosecond Bessel laser cutting of soda–lime glass and to achieve high-quality soda–lime glass cutting, a series of cutting experiments were conducted in this study. In this study, it was found that the machining point spacing, the incident laser energy, and the number of burst modes had a significant effect on the machining of the samples. The atomic force microscope (AFM) showed a better quality of roughness of the machined cross-section when the spacing of the machining points was 1 μm, a locally optimal solution was obtained when the number of burst modes was 2, and a locally optimal solution was also obtained when the incident laser power was 11.5 W. In this study, better machining quality was achieved for soda–lime glass of 1 mm thickness, with an average roughness of 158 nm and a local optimum of 141 nm.