Subject to an applied electric field, soft dielectrics with intrinsic low moduli can easily achieve a large deformation through the so-called electrostatic Maxwell stress. Meanwhile, the highly nonlinear electromechanical coupling between the mechanical and electric loads in soft dielectrics gives a variety of failure modes, especially pull-in instability. These failure modes make the application of soft dielectrics highly limited. In this paper, we investigate the large deformation, pull-in instability, and electroactuation of a graded circular dielectric plate subject to the in-plane mechanical load and the applied electric load in the thickness direction. The results obtained herein cover, as special cases, the electromechanical behaviors of homogeneous dielectrics. There is a universal physical intuition that stiffer dielectrics can sustain higher electromechanical loads for pull-in instability but achieve less deformation, and vice versa. We show this physical intuition theoretically in different homogeneous dielectrics and graded dielectrics. Interestingly, we find that the ability to sustain a high electric field or a large deformation in a stiff or soft homogeneous circular dielectric plate can be achieved by just using a graded circular dielectric plate. We only have to partly change the modulus of a circular plate, with a stiff or soft outer region. The change makes the same electromechanical behavior as that of a homogeneous dielectric, even increases the maximum electroactuation stretch from 1.26 to 1.5. This sheds light on the effects of the material inhomogeneity on the design of advanced dielectric devices including actuators and energy harvestors.