Large reasoning models (LRMs) have shown significant progress in test-time scaling through chain-of-thought prompting. Current approaches like search-o1 integrate retrieval augmented generation (RAG) into multi-step reasoning processes but rely on a single, linear reasoning path while incorporating unstructured textual information in a flat, context-agnostic manner. As a result, these approaches can lead to error accumulation throughout the reasoning chain, which significantly limits its effectiveness in medical question-answering (QA) tasks where both accuracy and traceability are critical requirements. To address these challenges, we propose MIRAGE (Multi-path Inference with Retrieval-Augmented Graph Exploration), a novel test-time scalable reasoning framework that performs dynamic multi-path inference over structured medical knowledge graphs. Specifically, MIRAGE 1) decomposes complex queries into entity-grounded sub-questions, 2) executes parallel inference paths, 3) retrieves evidence adaptively via neighbor expansion and multi-hop traversal, and 4) integrates answers using cross-path verification to resolve contradictions. Experiments on three medical QA benchmarks (GenMedGPT-5k, CMCQA, and ExplainCPE) show that MIRAGE consistently outperforms GPT-4o, Tree-of-Thought variants, and other retrieval-augmented baselines in both automatic and human evaluations. Additionally, MIRAGE improves interpretability by generating explicit reasoning chains that trace each factual claim to concrete paths within the knowledge graph, making it especially suitable for complex medical reasoning scenarios.