<p>Magnetic miniature robotic fish present significant potential for targeted drug delivery and non-invasive surgery. However, existing dynamic models assume constant stiffness, which restricts their capability to accurately capture the complex magnetically driven fluid–structure interactions with stiffness variation. This study proposes a novel magnetic miniature robotic fish featuring discrete stiffness variation, designed based on the tensegrity principle. The robot comprises a flexible head and a compliant tail connected through tensegrity rotational joints. The overall body stiffness is varied by adjusting the structural stiffness of the tensegrity joints. A data-driven dynamic model based on the Koopman operator is developed to address the challenges posed by nonlinear stiffness variations and magnetically induced multiphysics coupling. This model incorporates key physical factors, including magnetic field intensity, actuation frequency, and structural stiffness. The model’s distinctive capability lies in providing a unified dynamic representation across multiple stiffness configurations. By selecting optimal basis functions and regularization parameters, the model achieves a balanced trade-off between sparsity and predictive accuracy. The accuracy of the model is validated through straight-line swimming, turning swimming, and cross stiffness tests. Furthermore, simulations are performed to investigate the nonlinear effects of magnetic field intensity, frequency, and structural stiffness on swimming performance. The results reveal that the appropriate selection of these parameters enhances locomotion performance. A model predictive control framework is established based on the data-driven dynamics, and its potential for trajectory tracking is validated through multi-path swimming experiments.</p>