Jet propulsion is the main method of locomotion developed by cephalopods to swim through water, either for hunting or escaping from predators. Under this inspiration, diverse underwater robots utilizing jet propulsion-based locomotion are studied. This article presents a cephalopod-inspired robot based on a dielectric elastomer actuator, utilizing jet-propulsion actuation. The actuator is designed and optimized under the guidance of a corresponding electromechanical model. Then, the flow field characteristics of the synthetic jet actuator are simulated and analyzed. Equipped with the actuator, the bioinspired robot can locomote either with a speed of 0.66 body length per second on the surface of the water by jetting air or with a speed of 0.43 body length per second while almost completely submerged underwater by jetting water. The jet actuator presents even more environmental adaptability, which powers dual swimming locomotion by jetting two flow media, and can potentially be applied to the design of underwater robots.