Shape memory alloy (SMA) wire-based soft actuators have had their performance limited by the small stroke of the SMA wire embedded within the polymeric matrix. This intrinsically links the bending angle and bending force in a way that made SMA-based soft grippers have relatively poor performance versus other types of soft actuators. In this work, the use of free-sliding SMA wires as tendons for soft actuation is presented that enables large increases in the bending angle and bending force of the actuator by decoupling the length of the matrix and the length of the SMA wires while also allowing for the compact packaging of the driving SMA wires. Bending angles of 400° and tip forces of 0.89 N were achieved by the actuators in this work using a tendon length up to 350 mm. The tendons were integrated as a compact module using bearings that enables the actuator to easily be implemented in various soft gripper configurations. Three fingers were used either in an antagonistic configuration or in a triangular configuration and the gripper was shown to be capable of gripping a wide range of objects weighing up to 1.5 kg and was easily installed on a robotic arm. The maximum pulling force of the gripper was measured to be 30 N.