The outer portion of the rings of Saturn is probably immersed in intense particle radiation belts. We scale Pioneer 10 and 11 measurements to the Saturnian radiation belts and estimate that sputtering by high-energy protons from the ice particles in the outer portion of the rings leads to a net erosion rate there of 10-6 cm yr-1 after allowance for the rapid recapture, and thus the redistribution, of water molecules on the ring particles. The lifetime of ice particles in the outer portions of the rings against sputtering may then be less than the age of the solar system. We show that such water ice sputtering can maintain the neutral H atmosphere around the rings detected by Weiser et al. (1977). We also suggest that the very low albedo recently reported for the rings of Uranus could result from the sputtering away of primordial ices on the ring grains by Uranian radiation belt particles.