Laser technology is widely employed for chamfering phone screens and engraving telescope prisms. This study explores the use of high repetition frequency picosecond lasers to induce fractures in modified glass through a slit shaping method. The study demonstrates that an oblique cutting orientation facilitates precise crack propagation. The results indicate that the glass piece is 1.26 μm rough after separating and is sliced at a significant angle of 35° with the horizontal plane. In this study, the effects of laser pulse energy, pulse number, and scanning speed on the surface roughness and edge collapse of quartz glass are investigated. This novel cutting technique can resolve the issue of splitting and beveling prism glass, and it has a promising future in the area of laser processing translucent materials.