When immersed in an electrolyte, droplets of Ga-based liquid metal (LM) alloy can be manipulated in ways not possible with conventional electrocapillarity or electrowetting. This study demonstrates how LM electrochemistry can be exploited to coalesce and separate droplets under moderate voltages of ~1β10 V. This novel approach to droplet interaction can be explained with a theory that accounts for oxidation and reduction as well as fluidic instabilities. Based on simulations and experimental analysis, this study finds that droplet separation is governed by a unique limit-point instability that arises from gradients in bipolar electrochemical reactions that lead to gradients in interfacial tension. The LM coalescence and separation are used to create a field-programmable electrical switch. As with conventional relays or flip-flop latch circuits, the system can transition between bistable (separated or coalesced) states, making it useful for memory storage, logic, and shape-programmable circuitry using entirely liquids instead of solid-state materials