Dexterous manipulation is important for modern logistics automation. Industrial robots remain inferior to human labor in this area, especially in handling unknown objects in unstructured scenarios. It is observed that the human wrist contributes significantly to the dexterous manipulation capability by agilely changing the hand orientation to approach the target object and adjusting wrist stiffness to adapt to dynamic interaction. Inspired by the human wrist, we propose a novel soft wrist to achieve hybrid motion/stiffness control in a compact and lightweight structure. The dexterous motion and stiffness adjustment are simultaneously enabled by a novel multicable jamming mechanism, which is achieved by a precalibration of the relationship between stiffness with robot length and bending angle to adapt to both compliant and forceful tasks. Dedicated experiments were performed to validate its motion dexterity and variable stiffness property. A soft grasping system was developed to demonstrate the manipulation capability of the soft wrist by tasking it with automatic packaging, which is challenging for robots. Overall, the proposed soft wrist demonstrates a promising solution to enhance robotic manipulation capability to a human comparable level.