In this work, we propose a multi-field plate theory to study the magneto-mechanical behaviors of single- and multi-layered hard-magnetic soft material (HMSM) plates. First, the total energy functional for HMSM plates is established following the classical approach of the magnetostatic theory. Through variational calculations, the 3D governing equation system can be formulated, which is simplified by neglecting the effect of the activated magnetic field. The 2D vector plate equation is then derived from the 3D governing equations through a series expansion and truncation approach. The displacement and traction boundary conditions on the edges of plate samples are also proposed. Compared with the other plate or shell theories, the current plate theory naturally incorporates the elastic incompressibility and the magneto-mechanical coupling effect of the material, which doesn't involve any a priori hypotheses on the geometry and deformation of the plates. Thus, it is applicable for modeling the large deformations of hard-magnetic soft material plates. To show the efficiency of the plate theory, we study a benchmark problem, i.e., the plane-strain bending deformations of plate samples induced by magnetic and mechanical loads. Some analytical solutions of the plate equation system are derived, which provide accurate predictions on the magneto-mechanical response of the plate samples with different thickness-length ratios and magnetization directions. Based on the plate equation, the instabilities of the HMSM plates under magneto-mechanical loads can also be studied. To promote applications of the plate model, we further derive a simplified plate equation system and write out its weak form, which is then implemented into the finite element software. The efficiency of the simplified plate equation system is also verified through some typical examples. It is found that the numerical results obtained from the 2D plate model show good consistency with those of the 3D volume model, while the plate model exhibits obvious advantages in the aspects of numerical efficiency.