This paper investigates the dynamic modeling and vibration suppression of a flexible cantilever body with mobile control moment gyros (CMGs). A nonlinear dynamic model capturing the rigid-flexible coupling between the structure and the mobile CMG is systematically derived by Kane’s method. Vibration suppression is realized via the gyroscopic coupling caused by the direction change of the CMG’s angular momentum. To address the practical challenge of unmeasurable states, a neural network (NN)-based cascaded observer with a super-twisting differentiator is designed for real-time state estimation. A radial basis function (RBF) NN is used to approximate the nonlinear terms and disturbances in the system. Based on the observed states and the NN, a sliding mode controller based on the observer’s estimations is synthesized to achieve simultaneous trajectory tracking of the mobile CMG and active vibration suppression of the flexible structure. Numerical simulations demonstrate the effectiveness of the proposed method. Comparisons between the fixed CMG and mobile CMG are carried out to illustrate the advantages of the CMG acting as a mobile actuator.