Although cloud-based Large Language Models (LLMs) have significantly advanced complex multi-hop question answering, they pose severe data privacy risks. On the other hand, simply migrating such compute-intensive systems to edge devices with limited computational resources inevitably triggers context overload and the “lost-in-the-middle” phenomenon. To resolve the privacy-accuracy dilemma, we introduce DeARAG, a fully decoupled, local agentic framework. By shifting heavy hypergraph construction entirely offline, DeARAG substantially condenses the required context during inference. Consequently, the agent’s exploration is strictly grounded in the retrieved hypergraph topology, ensuring rigorous, evidence-based reasoning without overwhelming local resources. Evaluated on multiple datasets, our framework consistently outperforms massive, cloud-dependent baselines (e.g., achieving a gain of 6.47 F1 points on HotpotQA) using only consumer-grade GPUs, enabling highly precise on-device reasoning.