A new frictional mechanism, based on collective stick-slip motion of moiré superstructures across polycrystalline two-dimensional material interfaces, is predicted. The dissipative stick-slip behavior originates from an energetic bistability between low- and high-commensurability configurations of large-scale moiré superstructures. When the grain boundary separates between grains of small and large interfacial twist angle, the corresponding moiré periods are significantly different, resulting in forbidden grain boundary crossing of the moiré superstructures during shear induced motion. For small twist angle grains, where the moiré periods are much larger than the lattice constant, this results in multiple reflections of collective surface waves between the surrounding grain boundaries. In combination with the individual grain boundary dislocation snap-through buckling mechanism dominating at the low normal load regime, the friction exhibits nonmonotonic behavior with the normal load. While the discovered phenomenon is demonstrated for h-BN/graphene polycrystalline junctions, it is expected to be of general nature and occur in many other large-scale layered material interfaces.