Cyclic expansion-extrusion with an asymmetrical extrusion cavity (CEE-AEC) was performed on AZ31 magnesium alloy, and the effects of deformation passes on grain refinement, texture evolution, and mechanical properties were studied. The results show that during the CEE-AEC process, the continuous dynamic recrystallization (CDRX) and discontinuous dynamic recrystallization (DDRX) occur, and the average grain size reduces from 344 μm to 11.7 μm. The (0001) basal texture intensity gradually increases with the increase of processing passes. The existence of asymmetric cavities in CEE-AEC dies causes a great deflection of the basal texture. In addition, the mechanical properties of the alloy improve, and the tensile yield strength (TYS), ultimate tensile strength (UTS), and elongation (EL) are 109 MPa, 211 MPa, and 30.8%, respectively.