The gas desorption and secondary electron multiplication induced by electron bombardment tend to induce severe low-pressure discharge effects in space microwave device cavities. Nevertheless, few studies have focused on both secondary electron emission and electron-stimulated gas desorption (ESD). Although the suppression of secondary electrons by graphene was found to be better in our previous study, it is still unclear whether the surface modification of graphene, which brings about different interfacial states, can also be manifested in terms of ESD. The deep mechanism of gas desorption and secondary electron emission from this extremely thin two-dimensional material under electron bombardment still needs further investigation. Therefore, this paper investigates the mechanism of graphene modification on Cu metal surface on the gas release and secondary electron emission properties under electron bombardment. The surface states of graphene-modified Cu were characterized, and the ESD yield and secondary electron yield of Cu/GoCu were investigated using a self-researched platform and analyzed using molecular dynamics simulations and electron Monte Carlo simulations. The results of the study showed that the most released component on the Cu surface under the bombardment of electrons was H2O molecules, while the most released component on the GoCu surface was H2 molecules. The graphene-modified samples showed a significant suppression effect on the secondary electron yield and ESD only in the low-energy region below 400 eV. This study can provide a valuable reference for suppressing low-pressure discharge and multipactor phenomena in space microwave components.