Transcatheter Aortic Valve Replacement (TAVR) planning requires meticulous multimodal reasoning. However, adapting Multimodal Large Language Models (MLLMs) to this high-stakes domain is severely impeded by diagnostic hallucinations, where generated text lacks anatomical grounding. To address this, TAVR-VLM is introduced: a novel framework featuring Risk-Conditioned Causal Grounding Attention (R-CGA) that instantiates a model-internal ``Risk $\rightarrow$ Region $\rightarrow$ Word'' structural grounding pathway. R-CGA compresses multimodal inputs into a causal risk bottleneck, purifying dense visual features into a global risk mask. During autoregressive generation, a support-projected causal consistency objective constrains token-level grounding within the risk-defined support mask. Evaluated on $\text{M}^3\text{TAVR}$, a comprehensive 1,482-patient cohort, TAVR-VLM establishes a new state-of-the-art. It achieves an AUROC of 0.896, boosts CIDEr to 0.936, and drastically reduces the hallucination rate to 8.1\%, thereby improving interpretability for evidence-based surgical AI.