The room-to-low temperature (RT-LT) mechanical behavior of liquid oxygen-compatible epoxy composites (LOC-EP) is of great importance in the strength analysis of lightweight liquid oxygen tanks. This article first explores the tensile-compressive mechanical behaviors of LOC-EP from RT down to −183 °C. The results show that compared with RT, the tensile strength, compressive strength, and elastic modulus at −183 °C increase by 44%, 109%, and 160% respectively. Secondly, based on the theories of molecular chain freezing degree and yield surface extension, a ductile-brittle transition T of −60 °C and a completely brittle T of −90 °C are obtained sequentially. Moreover, a universal thermal-mechanical constitutive model for EP is derived, and the constitutive model parameters of LOC-EP from RT to −183 °C are fitted and calibrated using Matlab. Finally, the proposed constitutive model is introduced into Abaqus through a user subroutine. On the one hand, three-dimensional one-element analyses demonstrate that the simulation curves are highly consistent with the experimental and Matlab-fitted curves (errors less than 3%) with good convergence/accuracy. On the other hand, the fracture modes obtained from macroscopic simulations of tensile and compressive specimens are also coherent with the experimental fracture modes.