Magnesium alloys have been widely applied in the advanced fields of aerospace, medical implants, automobile, etc. However, the ignition risks of magnesium alloys, especially at high cutting temperatures, have to be considered in the machining process. This article conducts numerical investigations on the effects of cutting tools on the cutting behaviors, especially the cutting temperature of magnesium alloy AZ31B. The impacts of the rake angle, the tool edge radius, and the friction coefficient are studied by simulations based on the orthogonal cutting models using the DEFORM software. The simulation results are studied and compared to analyze the correlations between the cutting parameters and the cutting temperature, as well as the underlying mechanisms. The conclusions of this numerical analysis can provide specific guidance to the design of cutting tools for the magnesium alloys.