Piezoelectric metamaterials are capable of generating multifarious deformation modes, such as bending and torsion. Since piezoelectric modes are essentially gradient deformation combined with positive, negative, and zero electro-strains, current designs rely on combining cumbersome piezoelectric units with different polarization and multiple signals. Electric auxeticity is characterized by expansion in all directions, which can complement normal piezoelectric materials, exhibiting potential for simultaneous positive and negative electro-strains. However, conventional piezoelectric materials don’t possess electric auxeticity.In this report, we will propose the geometrically polarized design for auxetic piezoelectric metamaterials with single piezoelectric material fabrication and single-signal excitation. With the designed coupling between the mechanical deformation and geometrical polarization distribution, the electric auxetic effect has been realized. Furthermore, the electro-strains can be widely tuned from positive to negative via tailoring geometric parameters. Leveraging this characteristic, we achieve programmable multi-degree-of-freedom (multi-DOF) electro-mechanical modes, such as expansion-bending and bending-torsion modes. The piezoelectric metamaterial with intrinsic wave-shaped bending mode can serve directly as a robot to achieve smooth locomotion in wide and low frequency.