The effect of the distribution and concentration of rare earth (RE) element Y, crack orientation, temperature, and strain rate on the crack propagation behavior of the Mg alloys is investigated by molecular dynamics/Monte Carlo simulations. The results show that the RE element Y tends to form locally short-range order structures in the Mg alloys, and the introduction of the RE element Y can enhance the fracture toughness of the Mg alloys. The results indicate that with the increase of Y concentration, the crack propagation mode of the Mg alloys shifts from a mode, dominated by the dislocation emissions at the crack tip and the crack cleavage propagation to a mode dominated by the solid-state amorphization and the slip of amorphous bands. In addition, the results show that the faster the strain rate, the slower the crack propagation speed, and the crack propagation resistance increases with increasing temperature.