Mg alloys usually deform under complex biaxial compressive stress states (e.g. during drawing, forging and extrusion). In order to better understand how the biaxial compressive stress state influences the evolution of the microstructure and the deformation compatibility, the uniaxial and biaxial compression tests of AZ31 rolled sheets were performed at room temperature. The new self-developed biaxial compression devices offered a possibility to obtain the evolution of the microstructures by in situ measurements via electron backscatter diffraction. The analysis of geometrically necessary dislocation and the simulation based on the visco-plastic self-consistent method were used to examine the microscopic behaviors in the sheets during the uniaxial and biaxial compression tests. The results indicated that the reorientation of the texture during the biaxial compression was different from that during the uniaxial compression. The simulated results based on the visco-plastic self-consistent model suggested that the equivalent yield strength under a biaxial compressive stress state was lower than that under a uniaxial stress state. This was due to the higher relative activity of extension twins under biaxial compressive stress state. This also led to a lower geometrically necessary dislocation density in the biaxial compressed sample. The geometrically necessary dislocations were also more homogeneously distributed with a biaxial compressive stress state. The analysis of the activation of all the deformation mechanisms proved that the appearance of extension twinning variants limited the activation of prismatic slip during the uniaxial compression while promoting prismatic slip during the biaxial compression. This changeable interaction between extension twinning and prismatic slip combining with the lower geometrically necessary dislocations, the lower flow stress inferred that the application of the biaxial compressive stress state during processing at room temperature was a way to improve the deformability of Mg alloys.