Context. Sputtering serves as an important mechanism of atmospheric escape in the solar system. Aims. This study is devoted to atmospheric sputtering on Titan, with a special focus on how the N-2 and CH4 sputtering yields respond to varying ion incidence energy and angle, and varying ion mass. Methods. A Monte Carlo model was constructed to track the energy degradation of incident ions and atmospheric recoils from which the sputtering yields were obtained. A large number of model runs were performed, taking into account three categories of incident ion with representative masses of 1, 16, and 28 Da, as well as two collision models both characterized by a strongly forward scattering angle distribution, but different in terms of the inclusion or exclusion of electronic excitation of ambient neutrals. Results. Our model calculations reveal substantial increases in both the N-2 and CH4 sputtering yields with increasing ion incidence energy and angle, and increasing ion mass. The energy distribution of escaping molecules is described reasonably well by a power law, with an enhanced high energy tail for more energetic incident ions and less massive atmospheric recoils. The CH4-to-N-2 sputtering yield ratio is found to range from 10 to 20%, increasing with increasing incidence angle and also increasing with decreasing incidence energy. An approximate treatment of ion impact chemistry is also included in our model, predicting N-2 sputtering yields on Titan that are in broad agreement with previous results.