Core-excited fragmentation of SF6 is analyzed by using monochromatic synchrotron radiation and time-of-flight mass spectroscopy. Excitation of fluorine K and sulfur L levels yields highly dissociated and multiply charged ions such as SF2+, S2+ and S3+ that are not seen with valence level excitation. Excitation of sulfur L levels is found to be more dissociative than that of fluorine K levels in the sense that more atomic ions and more multiply charged sulfur ions are produced. In addition to the above results, the generation mechanism for these ions is discussed by considering the multistep Auger cascade decay of core holes.