This study presents a parametric optimization model for the friction disc of a combined friction face milling cutter operating under intensive contact friction, high clamping forces, and cyclic thermomechanical loading. The computational framework integrates ANSYS Workbench, the Static Structural module, Design of Experiments (DOE), Kriging surrogate modeling, and Multi-Objective Genetic Algorithm (MOGA) optimization. The friction disc geometry is defined by two design variables: the radial depth of the relief groove, a (3–6 mm), and its axial width, b (3–8 mm). Structural performance is evaluated using the von Mises equivalent stress and axial displacement of the cutting zone. Heat-treated 65G spring steel, with a yield strength of 640 MPa, is selected as the material. Using a safety factor of four, the allowable stress is limited to 160 MPa, while the permissible axial displacement is 0.05 mm to satisfy axial runout requirements for face milling cutters. Finite element analysis and response surface modeling show that parameter a predominantly affects axial deformation, whereas the combined influence of a and b governs the acceptable stress region. Multi-Objective Genetic Algorithm (MOGA) optimization identifies design solutions satisfying both strength and stiffness constraints. The proposed approach enables the determination of the minimum admissible values of the geometric parameters a and b while satisfying the prescribed strength, stiffness, and axial displacement constraints.