Ion bombardment of semiconductor substrates gives the possibility to generate ordered nanostructures by self-organization. Here, we investigated ion-beam induced morphology modifications of heteroepitaxial SiGe films on Si(001) that exhibit a distinct surface pattern as a consequence of strain-relief. Morphological changes and evolving surface nanostructures due to ion erosion were characterized by atomic-force microscopy. For SiGe films with mesa structures and for polycrystalline SiGe films, the existence of two characteristic energy regimes is shown. At an ion energy of 250 eV, roughening mechanisms take place. They result in an rms-roughness value exceeding the value of the initial sample surface. In the regime beyond 500 eV ion energy, the morphology smoothens and the pattern vanishes with increasing sputter depth. In both cases, a nanohillock formation in dependence of the sputter depth was found. The average diameter of the hillocks ranges between 14 and 27 nm. The possibility to generate hillocks on the nanometer scale by ion erosion demonstrates the potential of ion-bombardment induced nanopattern formation also for group IV semiconductor substrates.