Here, we investigate a scheme to realize free-space isolators and highly non-reciprocal mirrors with weak modulation imparted by an acoustic wave. We propose a strategy to dramatically break time-reversal symmetry by exploiting resonant interactions between a travelling acoustic wave and highly resonant Fabry–Pérot modes, inducing total reflection of an optical beam at a given angle, and no reflection at the negative angle. Different from conventional acousto-optic isolators, which are based on non-resonant frequency conversion and filtering, our proposal operates at the frequency of the optical signal by tailoring the resonant properties of the structure as well as the acoustic wave frequency and intensity, enabling 50 dB isolation with modest modulation requirements. Operation in the reflection mode allows for close-to-zero insertion loss, enabling disruptive opportunities in our ability to control and manipulate photons.