In high-power laser applications, it is common to use reflecting mirrors for controlling the beam, such as beam expansion, redirection and wavefront correction. However, various types of reflecting mirrors in the control system will absorb some of the light energy, forming a non-uniform temperature field, which cause deformation of the reflecting mirrors and ultimately affect the quality of the reflected beams. Since the support method and temperature field jointly determine the deformation of the reflecting mirrors, it is necessary to study the optimal support method for reflecting mirrors in the design of beam control systems. Based on thermoelastic mechanics, the methods to reduce the thermal deformation of reflecting mirrors using different mirror support methods are proposed, the temperature field and deformation of the reflecting mirrors under several common support constraints are quantified and simulated. The total deformation of the mirror, the relative deformation of the spot area, and the wavefront aberration introduced by the relative deformation of the spot area are compared. The results show that the support method with a small area constraint on the back of the reflecting mirror has the smallest relative deformation, and the support method with a rigid constraint on the back of the reflecting mirror has the largest relative deformation. The relative deformation of the mirror with a rigid constraint can be effectively reduced by about 98.4%. The experimental and simulation results are very close in terms of the relative deformation of the mirror in the beam spot area, and the wavefront images are essentially identical. These results provide theoretical support for the selection and design of mirror support in beam control systems.