The thermal compression deformation behavior of homogenized Mg–5Zn–1Mn (wt.%) alloy was systematically investigated over the temperature and strain rate ranges of 285–345 °C and 0.001–1 s−1, respectively. The constitutive model and thermal processing diagrams were established. The microstructure evolution process and dynamic recrystallization (DRX) mechanisms were analyzed. The results demonstrate that the flow stress curves of the ZM51 alloy exhibit prominent DRX characteristics. The peak stress can be improved by decreasing the deformation temperature or increasing the strain rate. A finite element simulation is performed, and the Arrhenius constitutive model can accurately depict the plastic flow process of the alloy with strain correction, and the average activation energy is about 143.821 kJ/mol. Both the percentage DRX and the DRX grain size are found to be sensitive to the applied deformation conditions, including temperature, strain rate, and true strain. The formation of DRX grains promotes the weakness of the texture and the refinement of the grains. Grain boundaries nucleation (including discontinuous and continuous DRX) and particle-stimulated nucleation (PSN) are the main DRX mechanisms. Based on the processing map, ZM51 alloy is suitable for large plastic deformation by multi-pass forging. The optimum processing temperature is 345 °C, and as the degree of plastic deformation increases, the strain rate can be suitably increased. Local plastic flow and microcracking at grain boundaries are the primary instability mechanisms of the alloy.