Magnetorheological (MR) dampers are widely used as semi-active energy-dissipation devices in structural vibration control. Traditional MR dampers, particularly their working mode, often struggle to achieve a high damping force output and sometimes fail to meet the needs of practical engineering. Therefore, it is necessary to study MR dampers that can provide a high damping force. This study proposes an MR damper that combines a built-in shear valve with various working modes of shear extrusion. The damper generates a higher damping force by applying a current to the coils at different positions and altering its working mode. First, the ANSYS Maxwell software simulates the internal magnetic circuit of the damper to assess whether the magnetic field intensity distribution and circuit direction meet the design requirements. Analysis revealed that the internal magnetic circuit distribution was reasonable and satisfied the operating requirements of the damper. Furthermore, the mechanical models of the two working modes were derived based on the Bingham and double-viscous models. Finally, the accuracies of the mechanical models were verified experimentally. The experimental results showed that the simulation values closely matched the experimental values under all the working conditions. Therefore, the proposed mechanical models are reasonable, and can provide significant reference values for practical engineering applications.