Volumetric Reasoning Segmentation (VRS) aims to segment a target region in a 3D medical scan from a free-form clinical query, where the referent is often implicit and requires both medical knowledge and volume-grounded reasoning. Existing methods typically rely on specialized segmentation tokens to connect language with mask decoding, but this coupling collapses the decision process into opaque latent representations, limiting interpretability and generalization to diverse narrative expressions. In this paper, we present MedVol-R1, a reinforcement learning-based framework for VRS that explicitly decouples evidence grounding from volumetric delineation: the LVLM grounds clinical reasoning to a verifiable 2D evidence anchor (key axial slice and 2D bounding boxes), which is then propagated into a coherent 3D mask by a frozen MedSAM2 module. We train MedVol-R1 with cold-start supervised fine-tuning followed by GRPO, guided by a multi-component reward that encourages informative evidence selection, accurate 2D spatial grounding, and cross-slice volumetric coherence, without requiring costly chain-of-thought annotations. Experiments on CT-ORG, AbdomenCT-1K, and KiTS23 from the M3D-Seg benchmark demonstrate that MedVol-R1 consistently outperforms strong baselines and achieves state-of-the-art performance, with reinforcement learning providing clear gains over pure supervised fine-tuning.