As a part of on-orbit services, the research on on-orbit capture has been receiving significant attention, given the increasing complexity of space activities and the growing number of spacecraft in orbit. The development of a high-adaptability and reliable capture manipulator is crucial due to the uncertainties involved in capturing space objects. Current manipulators face limitations in their capture principles and mechanical reliability, making it challenging to meet the requirements of modern space activities. To tackle this challenge, this paper proposes a novel deployable grasping manipulator, with the scissors-bending metamorphic cell as its core component. Just by introducing two variable kinematic pairs and several links into a typical scissors cell, deployment and envelope-bending with one degree of freedom (DoF) driving can be achieved. The cell metamorphic behaviors are analyzed through kinematic modeling, and its structural design is determined using the proposed bending radius and singularity design method. The integrated grasping manipulator is developed with a limb-reconfigurable design., A three-limb prototype is established for simulation and gravity-free grasping test, demonstrating its advantages of simple control, high kinematic reliability, grasping adaptability, and stability.