In this research work a material microstructure-level cutting model (MML cutting model) is presented. The crystal plasticity theory is adopted for modeling the cutting of the titanium alloy Ti–6Al–4V in orthogonal case. In this model, the grains of the studied material are explicitly presented, and their orientation angles and slip system strength anisotropy are considered as the main source of the microstructure heterogeneity in the cutting material. To obtain the material degradation process, the continuum self-consistent intragranular damage model and discrete cohesive zone inter-granular damage model, were developed, wherein the zero thickness cohesive element is implemented to simulate the bond between grain interfaces. This model was validated by a comparison with compression tests from literature. Results demonstrate the possibility to capture the influence of the microstructure on the material removal in terms of chip formation. Particularly, it is demonstrated that the grain orientation angle plays an important role for the chip segmentation and its periodicity during the cutting process