Mechanical stability and wear resistivity of graphene are prerequisite for its applications in nanomechanical devices. We employ atomic force microscopy based scratching in order to explore the wear of graphene at nanoscale, and the efficiency of graphene for the wear protection of an underlying substrate. We show that the wear of graphene consists of two processes: 1. the plastic eformation for lower normal loads, followed by 2. a sudden tearing of graphene for high enough normal load, with subsequent graphene peeling off from the substrate. The complete progress of the friction during these processes is measured and explained: the friction starts from low values on plastically deformed graphene, then strongly increases for a short time during graphene tearing, and ends up at lower value on uncovered substrate after graphene peeling. Finally, we demonstrate that around 5 nm thick (over ten layers) graphene flakes provide wear protection of the underlying substrate, while thin graphene flakes, around 1 nm thick (single and bilayer), can only enhance the mechanical capacity of the underlying substrate.