Based on the finite deformation theory, the virtual work theory, the updated Lagrange formula and the thermo-elastic-plastic constitutive equation, a coupled thermo-mechanical finite element model of metal minipore drilling process was established. Then, the minipore drilling process of a hard-to-cut material 1Cr18NigTi was simulated and experimentally studied. Some key techniques in the finite element simulation of metal cutting process, such as the material model, the chip separation, the damage criterion, and the dynamic mesh self-adaptive technology, were also discussed. Moreover, the chip formation in the twist drilling process was simulated by using the rigid plastic material model for workpieces and the thermal rigid model for tools. It is found that the simulated results accord well with the experimental ones, thus showing that the proposed finite element model is not only correct but also feasible in the prediction of the variations of drilling force, torque, and temperature with the feed.