Compared to the uniaxial stress loading of zirconium alloys, biaxial tensile stress is more complicated, and its influence on the deformation mechanisms and stretch formability of such alloys is rarely reported. In this study, uniaxial and biaxial tensile tests were performed on commercially pure zirconium with strong basal texture (BT) and weakened texture (WT) to clarify the deformation mechanisms occurring under different stress states by analyzing the microstructures, textures, and Schmid factors. The prismatic slip was found to be the dominant plastic deformation mechanism under uniaxial tensile stress, while it was suppressed under biaxial tensile stress in BT, and pyramidal slip was activated. Because the orientations of WT grains were dispersed, some of the grains under biaxial stress underwent both prismatic slip and tensile twinning to coordinate deformation, which improved the room-temperature stretch formability of WT, despite its low uniaxial elongation.