The effects of 1 MeV electron irradiation in air at a fixed accumulated dose and dose rates of 393.8, 196.9, 78.8, and 39.4 Gy s−1 on a shape memory epoxy (SMEP) resin were studied. Under low-dose-rate irradiation, accelerated degradation of the shape memory performance was observed; specifically, the shape recovery ratio decreased exponentially with increasing irradiation time (that is, with decreasing dose rate). In addition, the glass transition temperature of the SMEP, as measured by dynamic mechanical analysis, decreased overall with decreasing dose rate. The dose rate effects of 1 MeV electron irradiation on the SMEP were confirmed by structural analysis using electron paramagnetic resonance (EPR) spectroscopy and Fourier transform infrared (FTIR) spectroscopy. The EPR spectra showed that the concentration of free radicals increased exponentially with increasing irradiation time. Moreover, the FTIR spectra showed higher intensities of the peaks at 1660 and 1720 cm-1, which are attributed to stretching vibrations of amide CO and ketone/acid CO, at lower dose rates. The intensities of the IR peaks at 1660 and 1720 cm-1 increased exponentially with increasing irradiation time, and the relative intensity of the IR peak at 2926 cm-1 decreased exponentially with increasing irradiation time. The solid-state 13C nuclear magnetic resonance (NMR) spectra of the SMEP before and after 1 MeV electron irradiation at a dose of 1970 kGy and a dose rate of 78.8 Gy s-1 indicated damage to the CH2–N groups and aliphatic isopropanol segment. This result is consistent with the detection of nitrogenous free radicals, a phenoxy-type free radical, and several types of pyrolytic carbon radicals by EPR. During the subsequent propagation process, the free radicals produced at lower dose rates were more likely to react with oxygen, which was present at higher concentrations, and form the more destructive peroxy free radicals and oxidation products such as acids, amides, and ketones. The increase in peroxy free radicals at lower dose rates was thought to accelerate the degradation of the macroscopic performance of the SMEP.