Aims . Astrophysical ices on dust grain mantles in the interstellar medium (ISM) and dense circumstellar envelopes (CSEs) are continuously exposed to galactic cosmic rays (GCRs). In a laboratory setting, we studied the physical and chemical modifications of ice layers induced by energetic heavy ions as GCR analogues. The ice layers used have a molecular composition similar to that of icy grain mantles. Methods . Mixtures of H$_2$O:CO:CH$_3$OH molecules (percentages 73:24:3, 68:30:3, and 58:38:3) were condensed on a substrate at 15 K and irradiated with 40 MeV $^{58}$N$^{11+}$ ion beams. Irradiation-induced modifications were followed using the mid-infrared absorption spectroscopy technique. Results . We observed the evolution of infrared bands of CO$_2$ , HCO, HCOOH, CH$_4$ , H$_2$ CO,H$_2$O$_2$ , and more complex synthesised molecules. From the molecular column densities, cross-sections and sputtering yields were determined and compared to published results of water and carbon monoxide. Analysis of the chemical modifications reveals that the precursors are easily destroyed when they are in a molecular mixture, while others are desorbed. Conclusions . The main radiolitic modifications induced by GCR irradiations are molecular decomposition and sputtering. Extrapolation to astrophysical radiation conditions shows a strong dependence on the intensity of the GCR distributions at low energies, which allows the analysis of the ice evolution at timescales comparable to those of the ISM and CSE.