The galaxy phase-space distribution in galaxy clusters provides insights into the formation and evolution of cluster galaxies, and it can also be used to measure cluster mass profiles. We present a dynamical study based on $sim$3000 passive, non-emission line cluster galaxies drawn from 110 galaxy clusters. The galaxy clusters were selected using the Sunyaev-Zeldovich effect (SZE) in the 2500~deg$^2$ SPT-SZ survey and cover the redshift range $0.2 < z < 1.3$. We model the clusters using the Jeans equation, while adopting NFW mass profiles and a broad range of velocity dispersion anisotropy profiles. The data prefer velocity dispersion anisotropy profiles that are approximately isotropic near the center and increasingly radial toward the cluster virial radius, and this is true for all redshifts and masses we study. The pseudo-phase-space density profile of the passive galaxies is consistent with expectations for dark matter particles and subhalos from cosmological $N$-body simulations. The dynamical mass constraints are in good agreement with external mass estimates of the SPT cluster sample from either weak lensing, velocity dispersions, or X-ray $Y_X$ measurements. However, the dynamical masses are lower (at the 2.2$sigma$ level) when compared to the mass calibration favored when fitting the SPT cluster data to a $Lambda$CDM model with external cosmological priors, including CMB anisotropy data from Planck. The discrepancy grows with redshift, where in the highest redshift bin the ratio of dynamical to SPT+Planck masses is $eta=0.63^{+0.13}_{-0.08}pm0.06$ (statistical and systematic), corresponding to a $2.6sigma$ discrepancy.
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