There have been numerous efforts in processing metallic alloys into fine-grained materials, so as to exhibit high strain rate superplasticity (HSRSP) and/or low temperature superplasticity (LTSP). The current study applied the most simple and feasible one-step extrusion method on the commercial AZ31 magnesium ingot to result in HSR<SP. The one-step extrusion was undertaken using a high extrusion ratio at 250-350 • C, and the grain size after one-step extrusion became ∼ 1-4 µm. The processed AZ31 plate exhibited satisfactory room temperature tensile elongation of 30-50%; 200 • C elongations of 600% at 1 × 10 −4 s −1 and 425% at 1 × 10 −3 s −1 ; and 300 • C elongations of 900% at 1 × 10 −4 s −1 , 520% at 8 × 10 −3 s −1 , 300% at 2 × 10 −2 s −1 , and 210% at 1 × 10 −1 s −1 . This suggests that the current AZ31 Mg alloy has possessed HSRSP at relatively low temperatures of 280-300 • C, as well as LTSP at 200 • C. The low flow stress of 15-30 MPa and the true strain rate sensitivity of 0.3-0.4 both suggest that grain boundary sliding and solute drag creep have operated under these loading conditions. The current results imply that the simple high-ratio extrusion method might be a feasible processing mean for industry applications.