Water confined by hydrophilic materials shows unique transport properties compared to bulk water, thereby offering new opportunities for the development of nanofluidic devices. Recent experimental and numerical studies showed that nanoconfined water undergoes liquid- to solid-phase-like transitions depending on the degree of confinement. In the case of water confined by graphene layers, the van der Waals forces are known to deform the graphene layers, whose bending leads to further nonuniform confinement effects. Despite the extensive studies of nanoconfined water under equilibrium conditions, the interplay between the confinement and rheological water properties, such as viscosity, slip length, and normal stress differences under shear flow conditions, is poorly understood. The current investigation uses a validated all-atom nonequilibrium molecular dynamics model to simultaneously analyze the continuum transport and atomistic structural properties of water in a slit between two moving graphene walls under Couette flow conditions. A range of different slit widths and velocity strain rates are considered. It is shown that under subnanometer confinement, water loses the rotational symmetry of a Newtonian fluid. Under such conditions, water transforms into ice, where the atomistic structure is completely insensitive to the applied shear force and behaves like a frozen slab sliding between the graphene walls. This leads to the shear viscosity increase, although it is not as dramatic as the normal force increase that contributes to the increased friction force reported in previous experimental studies. On the other end of the spectrum, for flows at large velocity strain rates in moderate to large slits between the graphene walls, water is in the liquid state and reveals shear thinning behavior. In this case, water exhibits a constant slip length on the wall, which is typical of liquids in the vicinity of hydrophobic surfaces.