Graphene reinforced metal matrix nanocomposites hold significant potential owing to graphene’s exceptional mechanical and multifunctional properties. However, their practical application remains hindered by challenges such as weak interfacial bonding, mechanical anisotropy, and limited ductility. Inspired by origami design principles, this study introduces a nanocomposite architecture consisting of two identical graphene origami (GOri) layers embedded orthogonally within a copper (Cu) matrix, engineered to achieve in-plane mechanical isotropy and enhanced performance. Through molecular dynamics simulations, we systematically investigate its tensile behavior and underlying deformation mechanisms under various loading conditions. Our results show that the GOri/Cu nanocomposite retains an elastic modulus comparable to that of single-crystal Cu, while achieving markedly improved tensile strength and ductility. A distinctive three-stage tensile response is identified: an initial linear elasticity, followed by a quasi-zero stiffness plateau, and concluding with a strain-hardening stage. This behavior is accompanied by a pronounced negative Poisson’s ratio effect, attributable to the progressive unfolding of the embedded GOri. Parametric studies show that increasing the GOri content and external pressure amplifies the auxetic effect, while elevated temperatures reduce overall strength. Additionally, both the stress–strain response and Poisson’s ratio can be effectively tuned by modifying GOri geometry. This work offers valuable insights and design guidelines for the development of advanced nanocomposites with isotropic, auxetic, and energy-dissipative properties.