In the present work, Raman spectroscopy measurements and molecular dynamics simulations were used to investigate damage production in suspended single-layer graphene when irradiated by 23 MeV I, 3 MeV Cu and 18 MeV Cu beams. Despite the high energies of the used swift heavy ion beams, we found no evidence of ion track formation, i.e. all damage imparted to graphene was due to elastic collisions between ions and carbon atoms. Comparing experimental results with simulations, we conclude that a significant amount of energy (at least 40 % in the case of 23 MeV I irradiation) is dissipated away from graphene following the ion impact, and is a likely reason for the absence of ion tracks.