Supernumerary robotic limbs (SRL) are wearable extra limbs intended to help humans perform physical tasks beyond conventional capabilities in domestic or industrial applications. However, unique design challenges are associated with SRLs as they are mounted on the human body. SRLs must 1) be lightweight to avoid burdening the user, 2) be fast enough to compensate for human motions, 3) be strong enough to accomplish various tasks, 4) have high force-bandwidth and good backdrivability to control interaction forces. This paper studies the potential of a 3-DOF supernumerary robotic arm powered by magnetorheological (MR) clutches and hydrostatic transmission lines. The tethered configuration allows the power-unit to be located on the ground, which minimizes the mass worn (4.2 kg) by the user. MR clutches minimize the actuation inertia in order to provide fast dynamics and backdrivability. An experimental open-loop force-bandwidth of 18 Hz is founded at each joint and the maximal speed reached by the end-effector is 3.4 m/s, which is sufficient for compensating human motions. Also, the two first joints provide 35 Nm and the third joint, 29 Nm, which is strong enough to hold manual tools. Finally,the SRL is put in real practical situations, as fruit picking, painting, tools holding and badminton playing. The capability of the proposed SRL to perform successfully various tasks with high speed and smoothness suggests a strong potential of SRLs to become future commonly used devices.