The cold expansion technique effectively improves the strength of metallic structural joints. Based on the Johnson–Cook constitutive model, a simulation model for the mandrel extrusion strengthening process under stress wave loading is established. The effects of extrusion amount on damaged holes are analyzed based on residual stress peaks, strengthening zone distribution, and changes in inlet and outlet hole diameters. Results indicate that higher extrusion amounts increase tangential residual stress on the hole wall, while the strengthening zone expands radially and axially. Maximum axial residual compressive stress occurs 1.25 mm to 2.45 mm from the inlet. Tangential residual stress near the hole wall is compressive, gradually decreasing with distance, transitioning to tensile stress at approximately 1.8 mm radially, and eventually approaching 0 MPa. Further analysis reveals that increasing the extrusion amount results in a greater difference in hole diameter between the inlet and outlet. At smaller extrusion amounts, the deformation at both the inlet and outlet is minimal, with the outlet hole diameter changing significantly due to warping deformation compared to the inlet. Comparison results indicate that when the extrusion amount (E) is 4.0%, the difference in hole diameters between the inlet and outlet is small, while the strengthening zone is larger and the warping angle is smaller.