An extruded Mg-Al-Mn (AM30) magnesium alloy was subjected to uniaxial compression along the extrusion direction (ED) and the extrusion radial direction (RaD) at 450 °C and different strain rates. The microstructure and texture of the AM30 alloy under different deformation conditions were examined. Texture evolution was characterized by electron backscatter diffraction (EBSD). The activity of different deformation modes including twinning were simulated using the visco-plastic self-consistent (VPSC) and the simplistic Sachs polycrystal plasticity models. The results show that the microstructure and the mechanical property of the Mg alloy strongly depend on the strain rate, with twinning activated at strain rates >0.5 s−1. Dynamic recrystallization and twinning interacted with each other and affected the final microstructure and mechanical property of the magnesium alloy.