We mapped a 13 by 22 pc region in emission from 492 GHz [C I] and, for the first time, 551 GHz ^{13}CO(5-4) in the giant molecular cloud M17SW, using the Submillimeter Wave Astronomy Satellite. The morphologies of the [C I] and ^{13}CO emission are strikingly similar. The extent and intensity of the [C I] and ^{13}CO(5-4) emission is explained as arising from photodissociation regions on the surfaces of embedded molecular clumps. Modeling of the ^{13}CO(5-4) emission in comparison to ^{13}CO(1-0) indicates a temperature gradient across the cloud, peaking to at least 63 K near the M17 ionization front and decreasing to at least 20 K at the western edge of the cloud. We see no correlation between gas density and column density. The beam-averaged column density of C I in the core is 1x10^{18} cm^-2, and the mean column density ratio N(C I)/N(CO) is about 0.4. The variations of N(C I)/N(CO) with position in M17SW indicate a similar clump size distribution throughout the cloud.