A novel mechanism for actuating a miniature swimming robot is described, modeled, and experimentally validated. Underwater propulsion is obtained through the interaction of mobile internal permanent magnets that move a number of polymeric flaps arranged around the body of the robot. Due to the flexibility of the proposed swimming mechanism, a different range of performances can be obtained by varying the design features. A simple multiphysics dynamic model was developed in order to predict basic behavior in fluids for different structural parameters of the robot. In order to experimentally verify the proposed mechanism and to validate the model, a prototype of the swimming robot was fabricated. The device is 35 mm in length and 18 mm in width and thickness, and the forward motion is provided by four flaps with an active length of 20 mm. The model was able to correctly predict flap dynamics, thrust, and energy expenditure for magnetic dragging within a spindle-frequency range going from 2 to 5 Hz. Additionally, the model was used to infer robot-thrust variation related to different spindle frequencies and a 25% increase in flap active length. Concerning swimming performance, the proposed technical implementation of the concept was able to achieve 37 mm/s with 4.9% magnetic mechanism efficiency.