Managing large-scale vector datasets with disk-resident graph approximate nearest neighbor search (ANNS) systems incurs substantial storage overhead due to the co-location of vector data and auxiliary index metadata, which prevents the storage layer from exploiting their distinct compressibility. We present COMPASS, a component-aware compressed storage framework for disk-resident graph vector search. Leveraging data-index decoupling as a foundation, COMPASS losslessly compresses each component according to its distinct compressibility characteristics, thereby significantly reducing storage space. It further adapts the search and update paths to preserve their performance under compressed storage layouts. Evaluation on real-world public and proprietary billion-scale datasets shows that COMPASS reduces storage space by up to 58.7%, while delivering improved or competitive search and update performance compared to state-of-the-art disk-resident graph ANNS systems.