We report on a novel approach to cavity ring-down spectroscopy with the sample gas in saturated-absorption regime. This technique allows us to decouple and simultaneously retrieve the empty-cavity background and absorption signal, by means of a theoretical model that we developed and tested. The high sensitivity and frequency precision for spectroscopic applications are exploited to measure, for the first time, the hyperfine structure of an excited vibrational state of 17O12C16O in natural abundance with an accuracy of a few parts in 10{-11}.