In the present study, the mechanical response and deformation behavior of a Mg AZ31 plate with different types of pre-twins was systematically investigated under biaxial tension along the normal direction (ND) and transverse direction (TD) with different stress ratios. The results show that significant hardening was observed under biaxial tension. The yield values in the direction of larger stress values were higher than those under uniaxial loading conditions, and the solute atom segregation at twin boundaries generates more obvious strengthening effect. Noting that, for TRH (with cross compression along the rolling direction (RD) and TD and annealing at 180 °C for about 0.5 h) sample, the strength effect of the RD yield stress σRD:σND = 2:1 was higher than that of the ND yield stress under stress ratio σRD:σND = 1:2. There is a complex competition between twinning and detwinning under biaxal tension along the ND and TD of the pre-twinned samples with the variation in the stress ratio along the TD and RD. The variation in the twin volume fractions for all samples under biaxial firstly decreases and then increases with a higher stress ratio along the ND. As for the TDH sample (precompression along the TD and annealing), the changes of the twin volume fraction were lower than that of the TR sample (cross compression along the TD and RD). However, the amplitude of variation in twin volume fraction of the TRH sample is higher than that of the TR sample. This is because the relative activity of detwinning decreases and that of twinning increases, as the ND stress mainly leads to the growth of pre-twins and the TD stress often promotes detwinning of primary twins. With a higher stress ratio along the ND, the activity of twinning deformation increases and that of detwinning decreases.