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Protein-function prediction is crucial for elucidating molecular mechanisms driving biological processes and therapeutics development. Despite numerous computational tools demonstrating promising performance, they fall short when predicting rare, uncharacterized functions or indirect activities. Here, we present COSMOS, a context-aware Gene Ontology (GO) subgraph mining system for protein-function prediction. By leveraging inductive subgraph foundation models and an enriched knowledge graph of protein-GO relationships, COSMOS performs zero-shot, few-shot, and low-homology protein-function prediction. Built on 7,923,952 functional semantic relationships, COSMOS demonstrates robust capabilities to (1) generate state-of-the-art predictions for GO classes with sparse or no experimental annotations, (2) provide interpretable functional subgraphs for transparent rationale analysis, and (3) deliver complementary benefits when integrated with existing embedding-based prediction methods. We anticipate that COSMOS will serve as a complementary approach to conventional protein annotation methods and an interpretable tool for predicting protein functions within underexplored GO classes, thereby advancing genomics and therapeutic research.