Laser-assisted machining (LAM) is a promising technology for improving the machinability of hard-to-cut materials. In this study, based on the finite element method (FEM), a cutting model of thermally coupled non-uniform temperature field is established. The chip formation mechanism of fused silica during the laser-assisted machining process is explored from the aspects of laser power and laser incident angle. The results show that as the laser incident angle increases, the continuity of the chip increases gradually. An annular tool holder that can adjust the angle between the laser beam and the tool was designed. And the similar chip morphology obtained by variable-angle cutting experiments verified the effectiveness of the cutting model. Moreover, fracture chips and continuous banded chips are found in both simulation and experiment, which implies that the cutting mechanism works under a hybrid mode of brittle fracture and plastic deformation in the LAM process.