Large Language Models (LLMs) excel at many reasoning tasks but struggle with knowledge-intensive queries due to their inability to dynamically access up-to-date or domain-specific information. Retrieval-Augmented Generation (RAG) has emerged as a promising solution, enabling LLMs to ground their responses in external sources. However, existing RAG methods lack fine-grained control over both the query and source sides, resulting in noisy retrieval, shallow reasoning, and limited adaptability to heterogeneous knowledge sources. In this work, we introduce DeepSieve, a novel RAG method that incorporates information sieving via LLM-as-a-knowledge-router. DeepSieve breaks down complex queries into structured sub-queries and recursively routes each to the most appropriate knowledge source, filtering out irrelevant information through a multi-stage information sieving process. This modular and transparent approach ensures that DeepSieve remains adaptable across diverse information needs. Experiments on three multi-hop QA benchmarks involving heterogeneous sources show that DeepSieve achieves greater reasoning depth, retrieval precision, and interpretability compared to conventional RAG approaches. Our codes are available at https://github.com/MinghoKwok/DeepSieve.