Ten different simulation models are used to investigate the effects of content and chirality of graphene on the mechanical properties of nanolayered graphene/Cu composites. The increasing volume fraction of graphene can significantly enhance the Young's modulus and tensile strength of composites, but it leads to a lower yield strain. The negative Poisson's ratio of composites (NPRC) under uniaxial tension is observed at an atomic level. The corresponding mechanism is revealed by enhanced surface effect and inhomogeneous distribution of stress due to graphene-Cu interface. The strengthening mechanism of graphene is investigated by constraining effect in elastic region and blocking effect in plastic region. In a multi-layer structure, the middle copper film shows better tensile properties as its movement is constrained between two graphene layers. The blocking effect plays an important role in the interface interaction between graphene and dislocations. Graphene effectively blocks dislocations from penetrating through and restricts the synergistic movement of copper atoms.