Grasping and manipulating uncooperative objects in space is an emerging challenge for robotic systems. Many traditional robotic grasping techniques used on Earth are infeasible in space. Vacuum grippers require an atmosphere, sticky attachments fail in the harsh environment of space, and handlike opposed grippers are not suited for large, smooth space debris. We present a robotic gripper that can gently grasp, manipulate, and release both flat and curved uncooperative objects as large as a meter in diameter while in microgravity. This is enabled by (i) space-qualified gecko-inspired dry adhesives that are selectively turned on and off by the application of shear forces, (ii) a load-sharing system that scales small patches of these adhesives to large areas, and (iii) a nonlinear passive wrist that is stiff during manipulation yet compliant when overloaded. We also introduce and experimentally verify a model for determining the force and moment limits of such an adhesive system. Tests in microgravity show that robotic grippers based on dry adhesion are a viable option for eliminating space debris in low Earth orbit and for enhancing missions in space.