We perform dynamic compression to extruded AZ31 Mg alloys both along and perpendicular to the extrusion direction (ED) at a high strain rate of 1400 s−1 using split Hopkison pressure bar, and study the microstructure, texture evolution and mechanical anisotropy. We find that the temperature and loading direction play an important role in affecting microstructure evolution and flow stress. The mechanical anisotropy, yield strength and hardening ability are found to decrease with the rise of temperature. Moreover, the grains are also found to be refined remarkably, and the strong basal texture is weakened substantially owing to the dynamic recrystallisation especially in the case where dynamic compression is carried out perpendicular to the ED at 473 K.