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An active system consisting of many self-spinning dimers is simulated, and a distinct local rotational jamming transition is observed as the density increases. In the low density regime, the system stays in an absorbing state, in which each dimer rotates independently subject to the applied torque. While in the high density regime, a fraction of the dimers become rotationally jammed into local clusters, and the system exhibits spinodal-decomposition like two-phase morphologies. For high enough densities, the system becomes completely jammed in both rotational and translational degrees of freedom. Such a simple system is found to exhibit rich and multiscale disordered hyperuniformities among the above phases: the absorbing state shows a critical hyperuniformity of the strongest class and subcritically preserves the vanishing density-fluctuation scaling up to some length scale; the locally-jammed state shows a two-phase hyperuniformity conversely beyond some length scale with respect to the phase cluster sizes; the totally jammed state appears to be a monomer crystal, but intrinsically loses large-scale hyperuniformity. These results are inspiring for designing novel phase-separation and disordered hyperuniform systems through dynamical organization.