The three-dimensional (3D) graphene-based materials have raised significant interest due to excellent catalytic performance and unique electronic properties, while the preparation of uniform and stable 3D graphene structures remains a challenge. In this paper, using molecular dynamics simulations, we found that the nanotwinned copper (nt-Cu) matrix with small twin spacing can induce the wave-shaped wrinkling and sawtooth-shaped buckling graphene structures under uniaxial compression. The nt-Cu matrix possesses a symmetrical lattice structure for the lattice rotation with the dislocation annihilation, resulting in the transition of sandwiched graphene from 2D to 3D structures with good uniformity. The newly formed twin boundaries (TBs) in the nt-Cu matrix improve the resistance of graphene against the out-of-plane deformation so that graphene can maintain a stable wrinkling or buckling morphology in a wide strain range. These 3D texturing structures show great flexibility and their micro parameters can be controlled by applying different compressive strains. Furthermore, we propose a simple sliding method for decoupling graphene from the nt-Cu matrix without any damage. This work provides a novel strategy to induce and transfer the uniform wrinkling and buckling of graphene, which may expand the application of graphene in energy storage and catalysts.