Mixing of discretized states in quantum magnets has a radical impact on their properties. Managing this effect is key for spintronics in the quantum limit. Magnetic fields can modify state mixing and, for example, mitigate destabilizing effects in single-molecule magnets. The exchange bias field has been proposed as a mechanism for localized control of individual nanomagnets. Here, we demonstrate that exchange coupling with the magnetic tip of a scanning tunnelling microscope provides continuous tuning of spin state mixing in an individual nanomagnet. By directly measuring spin relaxation time with electronic pump-probe spectroscopy, we find that the exchange interaction acts analogously to a local magnetic field that can be applied to a specific atom. It can be tuned in strength by up to several tesla and cancel external magnetic fields, thereby demonstrating the feasibility of complete control over individual quantum magnets with atomically localized exchange coupling.