Handling dynamic objects is a significant challenge in robotics, necessitating the development of grippers capable of safe and reliable manipulation without compromising speed. Traditional rigid grippers, when used in dynamic environments, often produce excessive impact energy, posing risks to both the gripper and the object involved. Conversely, traditional soft grippers effectively absorb impact but suffer from slow response times, limiting their usability in dynamic tasks. Flexible gripping structures with bistable mechanisms combine the advantages of both, enabling rapid grasping while absorbing impact energy. However, most grippers with bistable structures show limited adaptability in their grasping capabilities and mostly utilize a single bistable mechanism for grasping functions. We present a novel multi-joint modular gripper that incorporates bistable structures to improve speed and adaptability. Our design employs bistable finger joint modules with elastic structures for swift action and Shape Memory Alloy (SMA) springs for recovery. This gripper utilizes 3D printing technology with flexible materials for rapid production. The gripper′s modularity allows for adjustments in grip size and mechanical properties by adding or removing modules, significantly expanding its operational range and adaptability. It can intercept a free-falling tennis ball within just 0.1 s. A comprehensive theoretical model and experimental verification validate the relationship between module design and performance, enabling precise control over the dynamic grasping capabilities of this innovative system. This modular approach not only addresses the limitations of existing soft grippers by enhancing their response times and adaptability but also paves the way for advanced robotic systems in manufacturing, healthcare, and beyond.