Thin-walled arc plate parts are widely used in aerospace critical equipment. However, such parts show inconsistent local stiffness at different locations under clamping, and their stiffness varies during the machining process, which brings difficulties in stable manufacturing. To address the problem, the discrete finite element model of a bilateral clamped thin-walled arc plate was established, and its position-associated stiffness distribution was obtained by Ansys Workbench. Subsequently, a discrete mirror milling simulation was carried out based on the “Element birth and death” method to investigate the its stiffness evolution under material removal. It turns out that under bilateral clamping, the stiffness of thin-walled arc plate exhibits a spatial “saddle-like” distribution with a gradient of change up to 54.38%, and the highest stiffness occurring in the position adjacent to the clamping area, while there is also an stiffness reinforcing zone in the center. During a single machining process, the local stiffness change of the workpiece shows non-monotonous positional correlation characteristics, and the central stiffness reinforcing zone still exists. With the deepening of the machining stage, the difference in stiffness between different positions further increases, with the maximum stiffness decreasing by about 69.97%, and the range of deformation reaches 0.2619 mm, which is a non-negligible influence on the machining accuracy.