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Context. The rate of sputtering and release of condensed species is an important aspect of interstellar chemistry, as is photodesorption for the most volatile species, because in the absence of such mechanisms the whole gas phase would have to condense in times often shorter than the lifetime of the considered medium, in particular for dense clouds. The recent detection of cyclic aromatic molecules by radioastronomy requires an understanding of the potential mechanisms supporting the rather high abundances observed. Aims. We perform experiments to advance our understanding of the sputtering yield due to cosmic rays for very large carbonaceous species in the solid phase. Methods. Thin films of perylene and coronene were deposited on a quartz cell microbalance and exposed to a 1.5 MeV N+ ion beam at the Laboratoire de Physique des 2 Infinis Irène Joliot-Curie (IJCLab, Orsay, France) and a 230 MeV 48Ca10+ ion beam at the GSI Helmholtzzentrum für Schwerionenforschung (GSI, Darmstadt, Germany). The mass loss was recorded as a function of the fluence for the N+ beam. The microbalance response was calibrated using Fourier transform infrared (FTIR) reflectance measurements of the produced films. In addition, the destruction cross-section of the same species was measured with the 48Ca10+ ion beam by in situ monitoring of the evolution of the infrared spectra of the bombarded films. Results. We deduced the sputtering yield for perylene and coronene and their radiolysis destruction cross-sections. Combining these results with a cosmic ray astrophysical spectrum, we discuss the impact on the possible abundance that may originate from the sputtering of dust grains with these molecules as well as from polycyclic aromatic molecules when they are trapped in ice mantles.