Many important chemical and biochemical processes in the condensed phase are notoriously difficult to simulate numerically. Often this difficulty arises from the complexity of simulating dynamics resulting from coupling to structured, mesoscopic baths, for which no separation of timescales exists and statistical treatments fail. A prime example of such a process is vibrationally-assisted charge or energy transfer. A quantum simulator, capable of implementing a realistic model of the system of interest, could provide insight into these processes in regimes where numerical treatments fail. Using trapped ions, we implement the building blocks of such a quantum simulation device and observe vibrationally-assisted energy transport between a donor and an acceptor ion. We tune our simulator into several parameter regimes and, in particular, investigate the transfer dynamics in the non-perturbative regime often found in biochemical situations.