The multiaxial deformation behavior of magnesium alloys is an important factor in understanding the service performance of structures. In the present research, the deformation mechanism of a Mg AZ31 sheet under biaxial tension with various stress ratios (σRD:σ45) along the rolling direction (RD) and the diagonal direction (45° direction) between the normal direction (ND) and transverse direction (TD) was systematically studied for the first time using cruciform specimens. The impacts of the stress ratio, σRD:σ45, on the mechanical response, twinning behavior, texture and slip behavior were investigated. The results showed that the contribution of twinning to plastic deformation was limited and governed by the Schmid law. The activation of twinning induced a twin texture component with c-axes largely parallel to the 45° between ND and TD. The deformation induced by biaxial tension was accommodated mainly by prismatic and basal slips under the stress ratio of σRD:σ45=4:1, and the fraction of grains favoring basal slip increased with lower stress ratio along the RD. The characteristics of flow stress can be effectively explained by the relative activities of twinning and slip with stress ratio.