The residual stresses state that a mechanical part obtained after machining is a crucial factor that impacts its in-service performance. This stress state is influenced by the thermomechanical loads exerted on the parts during the machining process, which are, in turn, determined by the tool parameters, process, and machining conditions. The aim of the present research was to anticipate how the cutting tool’s edge radius, rake angle, and clearance angle would affect the forces, temperature, and residual stresses induced while orthogonally cutting aluminum AA6061-T6. To achieve this, two-dimensional DEFORM™ software was utilized to develop a finite element model. The residual stresses trend results obtained demonstrated that rake angles of 0° and 17.5–20° values with a small edge radius (5 to 10 µm) and clearance angles of 7 and 17.5° values gave higher compressive stresses. The obtained simulated results were in good agreement with the experiments. The cutting forces, the temperature, and the maximum and minimum machining-induced residual stresses were found to be influenced more by the tool edge radius and the tool rake angle. The influence of the clearance angles on the above-mentioned machining responses was the least. Residual stresses can have a significant impact on the in-service performance of machined parts. The obtained results will help engineers select or design tools that promote a desired surface integrity during machining. This task is not obvious in practice because of difficulties in measuring residual stresses and also because the machining parameters and the tool geometry parameters have different and opposite impacts on thermo-mechanical loads, productivity, and on machining induced residual stresses.