The aim of the present research was to evaluate the effect of a support insert made of a silicone casting resin on reducing the post-machining deformation in thin walls made of 7050 T7451 aluminum alloy during finish milling at a maximized axial depth of cut. Experiments were conducted on the samples with 48 mm high walls and three different thicknesses (t = 1-2 mm, with the step of 0.5 mm), using three cutting speeds (vc = 300-900 m/min, with the step of 300 m/min). Statistical reliability of the obtained results was achieved through the application of a face-centered central composite design (FCCCD) and Response Surface Methodology (RSM). Post-machining deformation was evaluated based on flatness and wall thickness deviations that were measured via active scanning with a Zeiss Contura coordinate measuring machine. The results showed that an increase in the wall thickness reduced the post-machining deformation, while the impact of the cutting speed was nonlinear. The highest values of both flatness and wall thickness deviations were obtained using the mid-range cutting speeds, whereas significantly better results were produced at the extreme speeds (vc = 300 m/min and vc = 900 m/min). An examination of the surface in the thin-walled samples with a simple geometry revealed probably no presence of chatter. This finding is particularly important, as the tested parts had an open structure, which is exceptionally prone to chatter. The experimental findings indicate the effectiveness of using a support insert in thin-wall milling at a maximized depth of cut, demonstrating the solution’s potential in high performance machining for aerospace components.