Electron-stimulated desorption of hydrogen from the graphene/SiC(0001) surface at room temperature was investigated with ultrahigh vacuum scanning tunneling microscopy and ab initio calculations in order to elucidate the desorption mechanisms and pathways. Two different desorption processes were observed. In the high electron energy regime (4-8 eV), the desorption yield is independent of both voltage and current, which is attributed to the direct electronic excitation of the C-H bond. In the low electron energy regime (2-4 eV), however, the desorption yield exhibits a threshold dependence on voltage, which is explained by the vibrational excitation of the C-H bond via transient ionization induced by inelastic tunneling electrons. The observed current independence of the desorption yield suggests that the vibrational excitation is a single-electron process. We also observed that the curvature of graphene dramatically affects hydrogen desorption. Desorption from concave regions was measured to be much more probable than desorption from convex regions in the low electron energy regime (∼2 eV), as would be expected from the identified desorption mechanism.