The dynamical processes of a low-energy carbon ion collision with the graphene sheet supported by diamond at three impact positions are studied by using empirical potential molecular dynamics simulations. The energy transformation and the structural evolution have been studied. Five types of processes are observed: adsorption, hybridization, defects formation in diamond, atom emission and transmission. We find that the irradiation damage is closely related to the incident energy and impact position. In our simulations, as the projectile collides at a graphene atom, it transfers most of its energy to the primary knock-on atom, and defects are created in graphene. When the projectile moves perpendicular towards the center of a C-C bond in the graphene sheet, the energy transferred from the projectile to the atoms associated with the bond increases firstly and then decreases with the increasing incident energy, and the graphene sheet remains two-dimensional crystal structure after collision when the incident energy is larger than 360 eV. While the impact location is the center of a hexagonal ring on the graphene sheet, the energy transferred from the projectile to the atoms of the target ring is very small regardless of how large is the incident energy, and the graphene sheet is able to keep perfect crystal structure when the incident energy is larger than 34 eV.