The ultra-precision diamond cutting process exhibits strong size effects due to the ultra-small depth of cut that is comparable with the cutting edge radius. In the present work, we elucidate the underlying machining mechanisms of single crystal cerium under diamond cutting by means of molecular dynamics simulations, with an emphasis on the evaluation of the effect of depth of cut on the cutting process by using different depths of cut. Diamond cutting experiments of cerium with different depths of cut are also conducted. In particular for the smallest depth of cut of 0.2 nm, shallow cutting simulations varying the sharpness of the cutting edge demonstrate that an atomically sharp cutting edge leads to a smaller machining force and better machined surface quality than a blunt one. Simulation results indicate that dislocation slip is the dominant deformation mechanism of cerium under diamond cutting with each depth of cut. Furthermore, the analysis of the defect zone based on atomic radial distribution functions demonstrates that there are trivial phase transformations from γ-Ce to δ-Ce occurred in both the machined surface and the formed chip. It is found that there is a transition of material removal mode from plowing to cutting with the increase of the depth of cut, which is also consistent with the diamond cutting experiments of cerium with different depths of cut.