Hot compression tests were conducted on extruded Mg-Mn-Ce alloys under deformation temperatures of 723–873 K and strain rates of 0.0001–0.1 s^-1. Based on the obtained true stress-strain curve, the influence of deformation temperature and strain rate on material flow stress was analyzed. A constitutive relationship was established based on Arrhenius and BP-ANN models, and its accuracy was evaluated. Using the constitutive data obtained from the BP-ANN model, a hot processing map was plotted and numerical simulations were conducted. The results indicate that as the deformation temperature increases and the strain rate decreases, the flow stress of the alloy decreases. The BP-ANN model established has higher prediction accuracy, with a correlation coefficient of 0.9990 and an average relative error of only 2.69%. The hot working range of the alloy should be selected within the range of 0.001–0.01 s^-1 and 773–823 K. The numerical simulation and experimental results are in good agreement and can be used to guide the thermoplastic forming of alloys.