High-energy heavy ion irradiation is a very useful tool for the nanostructuring of 2D materials because defects can be introduced in a controlled way. This approach is especially attractive for the mass production of graphene nanomembranes when nanopore size and density can easily be tuned by ion irradiation parameters such as ion energy and applied fluence. Therefore, understanding the basic mechanisms in nanopore formation due to high-energy heavy ion impact is of the highest importance. In the present work, we used Raman spectroscopy to investigate the response of bilayer and trilayer graphene to this type of irradiation. Spectra obtained from graphene samples irradiated with 1.8 MeV I, 23 MeV I, 3 MeV Cu, 18 MeV Cu, and 12 MeV Si beams were analysed using the Lucchese model. It was found that the efficiency of damage production scales strongly with nuclear energy loss. Therefore, even for the most energetic 23 MeV I beam, the electronic energy loss does not contribute much to damage formation and ion tracks are unlikely to be formed.