Using atomic force microscopy, we have shown that friction on graphene/h-BN superlattice structures may exhibit unusual moire-scale stick slip in addition to the regular ones observed at the atomic scale. Such dual-scale slip instability will lead to unique length-scale dependent energy dissipation when the different slip mechanisms are sequentially activated. Assisted by an improved theoretical model and comparative experiments, we find that accumulation and unstable release of the in-plane strain of the graphene layer is the key mechanism underlying the moire-scale behavior. This work highlights the distinct role of the internal state of the van der Waals interfaces in determining the rich dynamics and energy dissipation of layer-structured materials.