We characterize multilayer graphene grown on C-face SiC before and after exposure to a total ionizing dose of 12 Mrad(SiO2) using a 10 keV x-ray source. While we observe the partial peeling of the top graphene layers and the appearance of a modest Raman D-peak, we find that the electrical characteristics (mobility, sheet resistivity, free carrier concentration) of the material are mostly unaffected by radiation exposure. Combined with x-ray photoelectron spectroscopy data showing numerous carbon-oxygen bonds after irradiation, we conclude that the primary damage mechanism is through surface etching from reactive oxygen species created by the x-rays.