The design of soft robots capable of navigation underwater has received tremendous research interest due to the robots' versatile applications in marine explorations. Inspired by marine animals such as jellyfish, scientists have developed various soft robotic fishes by using elastomers as the major material. However, elastomers have a hydrophobic network without embedded water, which is different from the gel-state body of the prototypes and results in high contrast to the surrounding environment and thus poor acoustic stealth. Here, we demonstrate a manta ray-inspired soft robot fish with tailored swimming motions by using tough and stiff hydrogels as the structural elements, as well as a dielectric elastomer as the actuating unit. The switching between actuated and relaxed states of this unit under wired power leads to the flapping of the pectoral fins and swimming of the gel fish. This robot fish has good stability and swims with a fast speed (∼10 cm/s) in freshwater and seawater over a wide temperature range (4-50 °C). The high water content (i.e., ∼70 wt %) of the robot fish affords good optical and acoustic stealth properties under water. The excellent mechanical properties of the gels also enable easy integration of other functional units/systems with the robot fish. As proof-of-concept examples, a temperature sensing system and a soft gripper are assembled, allowing the robot fish to monitor the local temperature, raise warning signals by lighting, and grab and transport an object on demand. Such a robot fish should find applications in environmental detection and execution tasks under water. This work should also be informative for the design of other soft actuators and robots with tough hydrogels as the building blocks.