Machine unlearning aims to erase requested data from trained models without full retraining. For Reasoning Multimodal Large Language Models (RMLLMs), this is uniquely challenging: intermediate chain-of-thought steps can still leak sensitive information even when final answers are forgotten, and overly aggressive interventions easily damage general reasoning ability. Yet no benchmark jointly evaluates how well unlearning methods suppress reasoning-level leakage while preserving reasoning competence. We address this gap with RMLLMU-Bench, the first benchmark for RMLLM unlearning that extends standard forgetting metrics with dedicated measures of reasoning leakage and reasoning retention. A systematic evaluation on RMLLMU-Bench reveals that existing unlearning methods for MLLMs and Large (Language) Reasoning Models (LRMs) either leave substantial leakage in the reasoning process or severely degrade reasoning performance. To address these gaps, we propose R-MUSE (Reasoning-preserving MLLM Unlearning via Subspace guidance and Adaptive Steering), a training-free and inference-time intervention framework that steers internal representations to forget both answers and reasoning traces while explicitly preserving general reasoning. Experiments on RMLLMU-Bench demonstrate that R-MUSE achieves a substantially better balance between effective forgetting and reasoning retention.