We study the rheology of suspensions of ice crystals at moderate to high volume fractions in a sucrose solution in which they are partially soluble, a model system for a wide class of crystal mushes or slurries. Under step changes in shear rate, the viscosity changes to a relaxed value over several minutes, in a manner well fitted by a single exponential. The behavior of the relaxed viscosity is power-law shear thinning with shear rate, with an exponent of −1.76±0.25, so that shear stress falls with increasing shear rate. On longer time scales, the crystals ripen (leading to a falling viscosity) so that the mean radius increases with time to the power 0.14±0.07. We speculate that this unusually small exponent is due to the interaction of classical ripening dynamics with abrasion or breakup under flow. We compare the rheological behavior to mechanistic models based on flow-induced aggregation and breakup of crystal clusters, finding that the exponents can be predicted from liquid phase sintering and breakup by brittle fracture.