The invention relates to a multiple-piece magneto-rheological fluid torque transferring device. The device has a multiple-piece layered structure, so that transferred torque is increased exponentially; the torque transferred by the device can be adjustable within a wide range by changing the current of a magnet exciting coil in the device; and under the condition that a driven shaft is fixed, the device can output adjustable and flexible torque which can be used as protecting links in a damper, a torsion applying device or a transmitting system. The device consists of a fixed supporting part, a driving rotor part, a driven rotor part, the magnet exciting coil, magneto-rheological fluid, a seal part and the like. The fixed supporting part consists of a left bearing end cap, a right bearing end cap, a shell left end cap, a shell right end cap, a left magnet yoke and a right magnet yoke. The driving rotor part and the driven rotor part consist of a driving shaft, driving discs, non-magnetic aluminum sleeves, a driven shaft and driven discs. The seal part comprises a dynamic seal ring, a seal ring baffle plate and a rubber oil seal. The multiple-piece magneto-rheological fluid torque transferring device has the characteristics of low energy consumption, wide torque adjustable range, sensitive response, excellent performance and the like.