The ion beam-induced removal of thin water ice films condensed onto Ag and bombarded by energetic Au, Au2, Au3, and C60 projectiles is examined both experimentally and with molecular dynamics computer simulations. For water overlayers of thicknesses greater than 10 A, the yields of sputtered Ag+ secondary ions decay exponentially with increasing ice thickness, revealing characteristic decay lengths of 24, 20, 18, and 7.0 A, respectively. It is shown that these values manifest the characteristic depths of projectile energy loss, rather than escape depths of the sputtered Ag atoms through the water ice overlayer. Computer simulations show that the mechanism of ejection involves the sweeping away of overlayer water molecules, allowing for an unimpeded escape of ejected Ag atoms. The relevance of these data with respect to surface sensitivity in secondary ion mass spectrometry is discussed.