The mirror component is one of the most critical components in the space remote sensing payload, and the performance of its support essentially determines the imaging quality of the system. Mirror components need to have high face shape accuracy, high reliability, and high stability. In this paper, taking the square mirror with the size of 550 mm × 450 mm as an example, we chose the Ultra-Low-Expansion Glass (Corning) as the mirror blank material, and through in-depth research on the principle of the three-point backside support and the engineering realization, we designed a three-point backside flexible support structure applied to the space mirror component. The design results were testified by simulation analysis; the results showed that with the mirror’s weight of 13.2 kg, the surface density can reach 48.5 kg/m2. For each gravity acceleration of 1 g, within the temperature range from 16 to 24 °C, carrying a forced displacement of 5 μm, the RMS value of the mirror component can reach 1/55λ (λ = 632.8 nm), which meets the requirement of high face shape accuracy of the mirror component in space. Finally, the mechanical test was carried out on the assembled mirror component, and the intrinsic frequencies of three directions of the mirror component were obtained through the test: 173.8 Hz, 176.4 Hz and 271.5 Hz, respectively. The changes of the mirror and its support structure were all less than 5″ after the 8 g sinusoidal vibration test and the 5.66 g random vibration test, which indicates that the flexible support structure meets the requirements of the high reliability of the space remote sensing loads and the high accuracy of the space mirror component. It shows that the flexible support structure meets the high reliability and high stability requirements of space remote sensing loads. The theoretical data and test results in this research can provide theoretical references for mirror components of the same size and type.