We present galaxy velocity dispersions and dynamical mass estimates for 44 galaxy clusters selected via the Sunyaev-Zel'dovich (SZ) effect by the Atacama Cosmology Telescope. Dynamical masses for 18 clusters are reported here for the first time. Using N-body simulations, we model the different observing strategies used to measure the velocity dispersions and account for systematic effects resulting from these strategies. We find that the galaxy velocity distributions may be treated as isotropic, and that an aperture correction of up to 7 per cent in the velocity dispersion is required if the spectroscopic galaxy sample is sufficiently concentrated towards the cluster centre. Accounting for the radial profile of the velocity dispersion in simulations enables consistent dynamical mass estimates regardless of the observing strategy. Cluster masses M_200_ are in the range (1-15)x10^14^M_{sun}_. Comparing with masses estimated from the SZ distortion assuming a gas pressure profile derived from X-ray observations gives a mean SZ-to-dynamical mass ratio of 1.10+/-0.13, but there is an additional 0.14 systematic uncertainty due to the unknown velocity bias; the statistical uncertainty is dominated by the scatter in the mass-velocity dispersion scaling relation. This ratio is consistent with previous determinations at these mass scales.