Hyperspectral imaging is an advanced technique for precisely identifying and analyzing materials or objects. However, its integration with robotic grasping systems has so far been explored due to the deployment complexities and prohibitive costs. Within this paper, we introduce a novel hyperspectral imaging-guided robotic grasping system. The system consists of PRISM (Polyhedral Reflective Imaging Scanning Mechanism) and the SpectralGrasp framework. PRISM is designed to enable high-precision, distortion-free hyperspectral imaging while simplifying system integration and costs. SpectralGrasp generates robotic grasping strategies by effectively leveraging both the spatial and spectral information from hyperspectral images. The proposed system demonstrates substantial improvements in both textile recognition compared to human performance and sorting success rate compared to RGB-based methods. Additionally, a series of comparative experiments further validate the effectiveness of our system. The study highlights the potential benefits of integrating hyperspectral imaging with robotic grasping systems, showcasing enhanced recognition and grasping capabilities in complex and dynamic environments.