We study the damping of collisionless Alfvénic turbulence in a strongly magnetised plasma by two mechanisms: stochastic heating (whose efficiency depends on the local turbulence amplitude
) and linear Landau damping (whose efficiency is independent of
), describing in detail how they affect and are affected by intermittency. The overall efficiency of linear Landau damping is not affected by intermittency in critically balanced turbulence, while stochastic heating is much more efficient in the presence of intermittent turbulence. Moreover, stochastic heating leads to a drop in the scale-dependent kurtosis over a narrow range of scales around the ion gyroscale.