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Context. The study of galaxy cluster mass profiles (M(r)) provides constraints on the nature of dark matter and on physical processes affecting the mass distribution. The study of galaxy cluster velocity anisotropy profiles (β(r)) informs the orbits of galaxies in clusters, which are related to their evolution. The combination of mass profiles and velocity anisotropy profiles allows us to determine the pseudo phase-space density profiles (Q(r)); numerical simulations predict that these profiles follow a simple power law in cluster-centric distance. Aims. We determine the mass, velocity anisotropy, and pseudo phase-space density profiles of clusters of galaxies at the highest redshifts investigated in detail to date. Methods. We exploited the combination of the GOGREEN and GCLASS spectroscopic data-sets for 14 clusters with mass M200 ≥ 1014 M⊙ at redshifts 0.9 ≤ z ≤ 1.4. We constructed an ensemble cluster by stacking 581 spectroscopically identified cluster members with stellar mass M∗ ≥ 109.5 M⊙. We used the MAMPOSSt method to constrain several M(r) and β(r) models, and we then inverted the Jeans equation to determine the ensemble cluster β(r) in a non-parametric way. Finally, we combined the results of the M(r) and β(r) analysis to determine Q(r) for the ensemble cluster. Results. The concentration c200 of the ensemble cluster mass profile is in excellent agreement with predictions from Λ cold dark matter (ΛCDM) cosmological numerical simulations, and with previous determinations for clusters of similar mass and at similar redshifts, obtained from gravitational lensing and X-ray data. We see no significant difference between the total mass density and either the galaxy number density distributions or the stellar mass distribution. Star-forming galaxies are spatially significantly less concentrated than quiescent galaxies. The orbits of cluster galaxies are isotropic near the center and more radial outside. Star-forming galaxies and galaxies of low stellar mass tend to move on more radially elongated orbits than quiescent galaxies and galaxies of high stellar mass. The profile Q(r), determined using either the total mass or the number density profile, is very close to the power-law behavior predicted by numerical simulations. Conclusions. The internal dynamics of clusters at the highest redshift probed in detail to date are very similar to those of lower-redshift clusters, and in excellent agreement with predictions of numerical simulations. The clusters in our sample have already reached a high degree of dynamical relaxation.