The spin–phonon coupling and the effects of strain on the ground-state phases of artificial SrMnO₃/BaMnO₃ superlattices were systematically investigated using first-principles calculations. The results confirm that this system has antiferromagnetic order and an intrinsic ferroelectric polarisation with the P4mm space group. A tensile epitaxial strain can drive the ground state to another antiferromagnetic–ferroelectric phase and then to a ferromagnetic–ferroelectric phase with the Amm2 space group, accompanied by a change in the ferroelectric polarisation from an out-of-plane direction to an in-plane direction. In contrast, a compressive strain could induce a transition from the antiferromagnetic insulator phase to the ferromagnetic metal phase.