Ti-Nb alloys are high-profile candidates for the biomedical applications. However, because of poor surface integrity (i.e. residual stress and surface roughness), Ti-Nb implantable medical devices need to be machined in order to obtain functional surfaces finish. In this work, experimental and numerical investigations are conducted to study the micro-cutting response of Ti42Nb titanium alloy produced by laser-based powder bed fusion. Experimental micro-cutting tests are carried out using precision turning lathe. Trials are performed with two cutting velocities of 60 m/min and 120 m/min and different feed rates, varying from 5 to 40 µm/rev. For the numerical study, a porous crystal plasticity-based model is proposed to address the impact of anisotropy and microstructure heterogeneities of the polycrystalline material. The crystal plasticity-based model is identified using strain-stress curves obtained from compression tests performed under two strain rates and a wide range of temperatures. Numerical micro-cutting simulations are performed in order to gain insight into the impact of microstructural features (i.e. crystallographic orientation and grain size) on the machinability of the alloy. According to the results, the effect of the strain rates and the temperature on the thermomechanical behavior of the Ti42Nb titanium alloy produced by laser-based powder bed fusion is correctly depicted. The model captured the strain localization on adiabatic shear band during compression tests. According to the micro-cutting simulations, the local variables such as temperature, damage and plastic deformation are strongly impacted by the crystallographic orientations and the grain size. In addition, depending on the crystallographic orientations, the chip morphology changes form continues, slightly segmented to largely segmented.