In this work, a hyperelastic constitutive model is developed to describe the thermo-mechanical behavior of the Ti17 titanium alloy. The grain shape and the crystallographic orientation are explicitly taken into account. The behavior of both theαandβphases is modelled with a crystal plasticity formulation coupled to a CDM (Continuum Damage Model). The constitutive model is implemented in the ABAQUS/Explicit finite element solver with a user-defined subroutine. The model parameters are identified from experimental tests. According to the cutting simulation results, both strain localization and chip segmentation are strongly impacted by the crystallographic orientation.