Like the Grand Canyon, Canyon de Chelley was cut from the terrain by the action of water erosion over the course of (perhaps) 500 million years.  Once the process starts, it creates a natural path for the water which then relentlessly hammers the sandstone year after year.  In the colder weather, water which has found its way under the surface freezes then thaws and breaks away chips of sandstone  This is a much faster process than erosion.

Given enough time, erosion can cut pretty deeply.