Epoxy resin (EP) and its composites have extensive applications in the nuclear industry. The study of their radiation effects can provide critical guidance in developing radiation-resistant epoxy resin materials. In this study, an epoxy resin was synthesized from tetrahydrophthalic acid diglycidyl ester and methylhexahydrophthalic anhydride. Boron nitride (BN) particles with two average particle sizes (7.5 μm and 757 nm) were used as filler to prepare two BN/epoxy resin composites. The possible bond cleavage of the crosslinking structural units of epoxy resin was investigated through density functional theory. The mechanical and thermal stability properties of the two BN/epoxy resin composites before and after gamma-ray irradiation under different absorbed doses were studied. The results showed that of all the chemical bonds consisting of a crosslinking structural unit, the C-C of the isopropyl unit had the minimum bond energy, making it easily breakable and leading to a breakdown of the polymer crosslinking network. When the absorbed dose exceeded 250 kGy, the tensile strength and thermal decomposition temperature of the epoxy resin and its composites noticeably decreased. The mechanical strength of the composite epoxy resins after irradiation depended on the combined effects of the BN particle size and the amount of added BN. When the absorbed dose reached 1 100 kGy, n-BN/EP with a mass fraction of 3% exhibited the highest tensile strength and thermal decomposition temperature. Therefore, adding a small amount of submicron-sized h-BN can improve the radiation resistance of epoxy resin. This work has theoretical and practical significance for the development of radiation-resistant epoxy resin composites.