The incorporation of graphene into nanotwinned copper is a promising approach to obtain a material with superior mechanical properties, while related research is rarely reported. In this study, we design several graphene/nanotwinned copper nanocomposites and investigate their compressive behaviors by molecular dynamics simulation. An unusual structural rearrangement is observed under compression at an atomic level. More specifically, graphene provides a supporting skeleton for the lattice rotation of nanotwinned copper under certain conditions, resulting in the annihilation of dislocations with the recovery of elasticity. Such a rearrangement process improves the strength and durability of the nanocomposites because of the intensive support provided by periodic graphene wrinkles and new twin boundaries. The interaction between graphene and nanotwinned copper matrix can be enhanced by decreasing twin spacing and introducing multilayer graphene. The symmetrical lattice orientation in the matrix, parallel graphene-twin boundaries, and a suitable compression direction collectively contribute to a perfect structural rearrangement.