As robotic arm applications expand beyond traditional industrial settings into service-oriented domains such as catering, household and retail, existing control algorithms struggle to achieve the level of agile manipulation required in unstructured environments characterized by dynamic trajectories, unpredictable interactions, and diverse objects. This paper presents a biomimetic control framework based on Spiking Neural Network (SNN), inspired by the human Central Nervous System (CNS), to address these challenges. The proposed framework comprises five control modules-cerebral cortex, cerebellum, thalamus, brainstem, and spinal cord-organized into three hierarchical control levels (first-order, second-order, and third-order) and two information pathways (ascending and descending). All modules are fully implemented using SNN. The framework is validated through both simulation and experiments on a commercial robotic arm platform across a range of control tasks. The results demonstrate that the proposed method outperforms the baseline in terms of agile motion control capability, offering a practical and effective solution for achieving agile manipulation.