The angular dependences of the sputter yield of (100) single crystal diamond under argon and oxygen ion beams were investigated. For argon ion beams a large increase in the sputter yield was observed as the angle of incidence was increased from the normal, with a maximum occurring at approximately 60° from the normal. The magnitude of the increase and the angle at which the maximum was observed were dependent on the ion energy and species. The shape of the yield versus angle of incidence curve indicated the presence of a highly damaged surface layer. Large deviations from this curve were observed where ion incidence was along channeling directions. Studies with oxygen ion beams showed almost no angular dependence for 500 eV ions while at an energy of 1000 eV the angular dependence was similar to that for argon ions. At normal incidence the yield for 500 eV oxygen ions was seven times larger than that for 500 eV argon ions. For 1000 eV oxygen and argon ions the corresponding ratio is only 2.5. Implications for mechanisms of inert and reactive ion etching are discussed. Application of the data to ion beam shaping of diamond tips for ultrahigh pressure research is discussed.