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A soft robot is presented which replicates the ability of cephalopods to travel in the aquatic environment by means of pulsed jet propulsion. In this mode of propulsion, a discontinuous stream of fluid is ejected through a nozzle and rolls into a vortex ring. The occurrence of the vortex ring at the nozzle-exit plane has been proven to provide an additional thrust to the one generated by a continuous jet. A number of authors have experimented with vortex thrusting devices in the form of piston-cylinder chambers and oscillating diaphragms. Here, the focus is placed on designing a faithful biomimesis of the structural and functional characteristics of the Octopus vulgaris. To do so, the overall shape of this swimming robot is achieved by moulding a silicone cast of an actual octopus, hence offering a credible replica of both the exterior and interior of an octopus mantle chamber. The activation cycle relies on the cable-driven contraction/release of the elastic chamber, which drives the fluid through a siphon-like nozzle and eventually provides the suitable thrust for propelling the robot. The prototype presented herein demonstrates the fitness of vortex enhanced propulsion in designing soft unmanned underwater vehicles.