CircRNA-miRNA interaction (CMI) plays a pivotal role in disease therapeutics and drug discovery. However, existing methods face several challenges in modeling complex biological networks and zero-shot learning scenarios. Biological networks encapsulate rich biological information, yet current approaches often fail to fully exploit this depth. Moreover, zero-shot prediction requires models to identify new interactions without relying on previously observed samples, imposing stringent requirements on generalization capabilities. To address these limitations, we propose a dual-channel learning framework leveraging State space modeling for Zero-shot CMI prediction (ZeroStem). ZeroStem first enhances the biological relevance of node using prior knowledge, and employs a graph Transformer to extract macro-topological representations. Subsequently, it generates semantic subgraphs based on meta-paths to focus on specific biological relationships, utilizing the Mamba to extract micro-semantic representations via state space modeling. Finally, macro-topological and micro-semantic representations are seamlessly integrated through linear transformation and residual connections, enabling high-precision zero-shot CMI prediction. Extensive experiments on multiple benchmark datasets demonstrate that ZeroStem significantly outperforms existing methods, validating its efficiency and robust generalization in CMI prediction. Case studies further illustrate that ZeroStem offers novel insights into the molecular mechanisms underlying intricate disease-associated networks.