Multiferroics have found renewed interest in topological magnetism and for logic-in-memory applications. Among them, SrMnO3, possessing strong magnetoelectric coupling, is gaining attention for the design of coexisting magnetic and polar orders upon straining. Here we demonstrate antiferromagnetic exchange interactions in strained SMO thin films extracted from a new feature in the phase response of spin Hall magnetoresistance, which has not been explored in earlier works, such as in magnetic insulators. We explain our findings with a model that incorporates magnetic anisotropy along the  direction, corroborates with density functional theory studies, and is consistent with the direction of ferroelectric polarization in SrMnO3. The fundamental insights obtained from our studies establishes the potential of this material in magnetoelectrically coupled devices for different logic and memory applications.