During the thermo-mechanical coupled analysis of twist drills, to address the instability of the traditional NS-RPIM method and further improve computational accuracy, this paper employs a stable node-based smoothed radial point interpolation method (SNS-RPIM) for the numerical simulation and analysis of twist drills. This method obtains the system stiffness matrix by using stabilization terms related to the field variables, then establishes the discrete system equations using the smoothed Galerkin weak form to solve for the temperature, stress, and displacement of the twist drill. Comparing the displacement, temperature, stress, and computational efficiency of SNS-RPIM with NS-RPIM and traditional FEM, Results proved that the introduction of the stabilization term made the SNS-RPIM had a ‘close-to-exact’ stiffness, thereby solving the ‘overly-soft’ in the traditional node-based smoothed radial point interpolation method (NS-RPIM). SNS-RPIM was in good agreement with the reference solution when using the same fewer nodes as finite element method (FEM), and the errors were much smaller than those of FEM. Moreover, SNS-RPIM performed better than NS-RPIM and FEM when processing distorted meshes. Therefore, the developed method showed great potential in Thermal Elastic–Plastic problems.