This paper investigates the nonlinear bending behavior of sandwich plates with functionally graded auxetic 3D lattice core. First and foremost, an auxetic 3D lattice metamaterial with negative effective Poisson’s ratio (EPR) is designed and examined via theoretical and finite element methods with experimental verifications using specimens fabricated by 3D printing. Furthermore, three functionally graded configurations of the auxetic 3D lattice core through the plate thickness direction are proposed and compared with the uniform distribution case. Full-scale finite element modeling and nonlinear thermal-mechanical analysis are performed for the sandwich plates, with the temperature-dependent material properties of both core and face sheets taken into account. Numerical results revealed that the auxetic core can remarkably reduce the lateral deflections, with comparison to their non-auxetic counterpart with positive EPR. Parametric studies are further carried out to demonstrate the effects of functionally graded configurations, temperature rises, facesheet-to-core thickness ratios, boundary conditions, and strut radii on the nonlinear bending load-deflection curves, along with EPR-deflection curves in the large deflection region.