The infrared opto-mechanical system can improve detection sensitivity by working in a cryogenic environment to reduce background radiation, which causes many technical challenges for mirror assembly structure design. In a cryogenic environment, different coefficient of thermal expansion (CTE) of the mirror and the connector cause the surface accuracy change to be the main problem. Design the structure of the.450 mm mirror assembly working at 240 K. The mirror material is SiC, and the connector material is Invar. The support method is rear support in the center. Great flexibility is designed for the connector to improve surface accuracy. Further, the main design parameters are optimized and analyzed. The influence curves on the surface accuracy are obtained. The root mean square (RMS) of gravity along the optical axis is 8.585 nm, the RMS along the radial direction is 3.710 nm, and the RMS is 5.086 nm working at 240 K. The first order frequency is 277 Hz, and the lightweight rate is 89.4%.