The redundant free-flying space manipulator (RFFSM) has emerged as a major research focus, providing enhanced operational flexibility and robustness for increasingly complex tasks, while the whole-body coordinated control under unstructured environments and multiple complex safety constraints is still a critical challenge. To this end, this article presents a novel hierarchical safety-critical control framework for the RFFSM, explicitly modelled on the Special Euclidean group SE(3), to perform whole-body coordinated control in the task space. A robust nominal controller is developed to simultaneously control the spacecraft base and the end-effector (EE) in the task space based on the full pose configuration error defined on SE(3), integrated with a disturbance observer (DOB) to actively compensate for external disturbances. In addition, a robust rectified control barrier function (R2eCBF) is presented to enforce safety constraints, including joint angle limits, singularity avoidance, and whole-body collision avoidance constraints, and is further integrated into the safety filter through quadratic programming (QP) to modify the nominal control in a minimal way. The effectiveness and superiority of the proposed method are validated through comparative simulations on a free-flying space robot mounted with a 7-DOF manipulator, demonstrating enhanced safety and robust performance. © © 2025. Published by Elsevier Masson SAS.