The Full-disc vector MagnetoGraph (FMG) is one of the payloads deployed in the Advanced Space-based Solar Observatory (ASO-S). As an important part of the FMG image stabilization system, the tip/tilt mirror will determine the observational performance of the payload. Therefore, it is necessary to analyze the mechanical performance of the tip/tilt mirror. In this paper, we design a side-fixed flexible supporting mirror structure, of which the supporting force is provided by elastic presser, and the force can be changed by adjusting the thickness of mirror shims. In order to determine the appropriate thickness setting, we construct 3 models with different parameters. For each model, we simulate static analysis and transient dynamic analysis at 100Hz and pm0.1mrad in zero gravity field by finite element software. The effect of gravity on the surface is also considered. Simulation results show that the designed tip/tilt mirror meets the performance requirements of the optical systems, PV (Peak-Valley) $<$ 1/10 wavelength, RMS (Root Mean Square) $<$ 1/40 wavelength, and gravity has no significant effect on the surface. Based on the simulation results, we further process, assemble, and test one of the models. Test results verify that the design of the tip/tilt mirror structure is satisfactory, and the simulation results are valid.