Vagus nerve stimulation (VNS) is emerging as potential treatment for several chronic diseases. However, limited control of fiber activation, e.g., to promote desired effects over side effects, restricts clinical translation. Towards that goal, we describe a VNS method consisting of intermittent, interferential sinusoidal current stimulation (iCS) through multi-contact epineural cuffs. In experiments in anesthetized swine, iCS elicits nerve potentials and organ responses, from lungs and laryngeal muscles, that are distinct from equivalent non-interferential sinusoidal stimulation. Resection and micro-CT imaging of a previously stimulated nerve, to resolve anatomical trajectories of nerve fascicles, demonstrate that iCS responses are explained by activation of organ-specific fascicles rather than the entire nerve. Physiological responses in swine and activity of single fibers in anatomically realistic, physiologically validated biophysical vagus nerve models indicate that iCS reduces fiber activation at the interference focus. Experimental and modeling results demonstrate that current steering and beat and repetition frequencies predictably shape the spatiotemporal pattern of fiber activation, allowing tunable and precise control of nerve and organ responses. When compared to equivalent sinusoidal stimulation in the same animals, iCS produces reduced levels of a side-effect by larger laryngeal fibers, while attaining similar levels of a desired effect by smaller bronchopulmonary fibers.