For 80 MN forging hydraulic press, a specialized mechanical arm for punching large-scale ring forgings was designed to replace manual operation based on the punching process of blank during its operation. Then, in order to ensure that the design of mechanical arm meets the requirements of strength and stiffness, the static analysis on the mechanical arm was conducted to verify the rationality of design scheme. The analysis results show that the strength on the mechanical arm meets the material requirements, but there is still a large optimization space. Therefore, the lightweight design on the mechanical arm was conducted by the response surface method. According to the results of static analysis, taking four size parameters as the optimization variables, the maximum deformation and equivalent stress as the constraint conditions, and the minimum total weight as the goal, the mathematical model was established. By optimizing and screening candidate points, rounding their dimensions and reanalyzing them, after comparison, the weight is reduced by 421 kg, the weight reduction ratio is up to 15.22%, and the optimization effect is significant.