In order to ensure the surface accuracy of the Pointing, Acquisition and Tracking (PAT) mirror in the harsh space environment, a flexible support structure with grooves on the bottom was designed. Due to the large number of parameters of flexible support structure, in order to avoid serious coupling between parameters, the orthogonal optimization method was used to optimize the parameters of flexible support structure, and then the finite element method was used to analyze the mechanical and thermal characteristics of mirror components. The simulation results show that the first-order frequency of the mirror module is 352.61 Hz, and the maximum surface error RMS under the combined action of 1 g gravity and 10 ℃ temperature rise (temperature drop) is λ/54.79(λ=632.8 nm), which can satisfy the dynamic and static stiffness and thermal dimensional stability. The ZYGO interferometer is used to detect the mirror surface shape in the temperature range of (20±10) ℃. The results show that the PV value of the mirror surface is better than λ/6, and the RMS is better than λ/43, which meets the requirement of RMS≤λ/40. The experimental results show that the design of flexible support parameters is reliable and meets the application requirements.