This study aims to improve the impact protection performance of composite structures by combining a honeycomb core with negative Poisson’s ratio and graphene platelets reinforced (GPR) face sheets. The paper investigates the nonlinear repeated low-velocity impact responses of auxetic honeycomb composite plates, taking into account loading-unloading-reloading processes. Effective material properties of the auxetic honeycomb core and GPR face sheets are obtained by using the proposed modified Gibson function and Halpin–Tsai model. Then, taking into account geometric nonlinearity, the nonlinear equations of motion for the system were derived by Hamilton's principle. Afterward, the time-varying contact force between the composite plate and a spherical impactor is defined by the modified nonlinear Hertz contact theory. The Galerkin method and variable-step Runge–Kutta algorithm are selected to obtain nonlinear impact responses. The proposed methods are verified by finite element simulation and experiment. Finally, the study evaluates the effects of key parameters on the nonlinear repeated low-velocity impact responses.