In order to reduce the influence of temperature deformation of large-size body-mounted radiators on the observation accuracy of space station telescopes and adapt to launch vibration loads, this paper proposes a floating combination stress release mechanism. Firstly, based on the dimensions, operating conditions, and stress directions of the radiator, an “orthogonal + parallel” layout of the radiator stress release mechanism is designed. To verify whether the layout design complies with the fully constrained theory, the layout design model is simplified into a four-point model, including one fixed support, two line-degree-of-freedom release mechanisms, and one plane-degree-of-freedom release mechanism. Degree-of-freedom analysis is conducted, and the statically determinate support goal is successfully achieved. Then, through the layout design of the stress release mechanism, specific modeling designs are carried out for the fixed support, line-degree-of-freedom release mechanisms, and plane-degree-of-freedom release mechanism using three-dimensional modeling software. Finally, the feasibility of the design scheme is verified through finite element simulation and mechanical testing. The results show that under sine and random vibrations, the maximum response amplification factor is 4.2, which meets the design requirement of being less than five. The maximum stress is 192 MPa, which is lower than the material’s yield limit. Under the application of an 80 °C temperature difference, the displacement response value of the radiator is 3.28 mm. This value falls within the allowable movement range of the stress release mechanism and meets the design criteria.