Sawtooth behavior has been investigated in plasmas heated with off-axis neutral beam injection in ASDEX Upgrade [A. Herrmann and O. Gruber, Fusion Sci. Technol. 44 , 569 (2003)] and the Mega-Ampere Spherical Tokamak MAST [A. Sykes and et al. , Nucl. Fusion 41 , 1423 (2001)]. Provided that the fast ions are well confined, the sawtooth period is found to decrease as the neutral beam is injected further off-axis. Drift kinetic modeling of such discharges qualitatively shows that the passing fast ions born outside the q =1 rational surface can destabilize the n =1 internal kink mode, thought to be related to the sawtooth instability. This effect can be enhanced by optimizing the deposition of the off-axis beam energetic particle population with respect to the mode location.