To ensure the high surface accuracy and high thermal stability of space mirror, a lightweight design for the Phi 514mm ULE primary mirror of a space remote sensor and flexible support structure with three-point was carried out. By further optimizing the parameters of the flexible supporting structure, the requirements of the optical index were met. The finite element model of the mirror assembly was established, and the static and dynamic characteristics of the assembly were analyzed. The results showed that the surface shape accuracy (RMS) of the mirror assembly is better than 8 nm under a load case of 1g gravity when the optical axis is level, and the first-order natural frequency of the component is 254 Hz. Finally, a mechanical test was carried out on the mirror assembly. The test results showed that the first-order frequencies of the three directions of the mirror assembly are all greater than 100 Hz, the error between the test data and the finite element analysis results does not exceed 10%. Analysis and test results showed that, the reasonable support structure design can effectively lower the change of the mirror surface shape caused by assembly stress and thermal stress, and has good dynamic performance. It is verified that the mirror and its supporting structure designed in this paper are reasonable, which provides reference and ideas for the design of flexible supporting structure of similar space mirror.