Many of the proposed future applications of graphene require the controlled introduction of defects into its perfect lattice. Energetic ions provide one way of achieving this challenging goal. Single heavy ions with kinetic energies in the 100 MeV range will produce nanometer-sized defects on dielectric but generally not on crystalline metal surfaces. In a metal the ion-induced electronic excitations are efficiently dissipated by the conduction electrons before the transfer of energy to the lattice atoms sets in. Therefore, graphene is not expected to be irradiation sensitive beyond the creation of point defects. Here we show that graphene on a dielectric substrate sustains major modifications if irradiated under oblique angles. Due to a combination of defect creation in the graphene layer and hillock creation in the substrate, graphene is split and folded along the ion track yielding double layer nanoribbons. Our results indicate that the radiation hardness of graphene devices is questionable but also open up a new way of introducing extended low-dimensional defects in a controlled way.