The Greenland ice sheet (GrIS) covers a complex network of canyons thought to be preglacial and fluvial in origin, implying that these features have influenced the ice sheet since its inception. The largest of these canyons terminates in northwest Greenland at the outlet of the Petermann Glacier. Yet, the genesis of this canyon, and similar features in northern Greenland, remains unknown. Here, we present numerical model simulations of early GrIS history and show that interactions among climate, the growing ice sheet, and preexisting topography may have contributed to the excavation of the canyon via repeated catastrophic outburst floods. Our results have implications for interpreting sedimentary and geomorphic features beneath the GrIS and around its marine margins, and they document a novel mechanism for landscape erosion in Greenland.