Surgical workflow recognition is vital for automating tasks, supporting decision-making, and training novice surgeons, ultimately improving patient safety and standardizing procedures. However, data corruption can lead to performance degradation due to issues like occlusion from bleeding or smoke in surgical scenes and problems with data storage and transmission. In this case, we explore a robust graph-based multimodal approach to integrating vision and kinematic data to enhance accuracy and reliability. Vision data captures dynamic surgical scenes, while kinematic data provides precise movement information, overcoming limitations of visual recognition under adverse conditions. We propose a multimodal Graph Representation network with Adversarial feature Disentanglement (GRAD) for robust surgical workflow recognition in challenging scenarios with domain shifts or corrupted data. Specifically, we introduce a Multimodal Disentanglement Graph Network that captures fine-grained visual information while explicitly modeling the complex relationships between vision and kinematic embeddings through graph-based message modeling. To align feature spaces across modalities, we propose a Vision-Kinematic Adversarial framework that leverages adversarial training to reduce modality gaps and improve feature consistency. Furthermore, we design a Contextual Calibrated Decoder, incorporating temporal and contextual priors to enhance robustness against domain shifts and corrupted data. Extensive comparative and ablation experiments demonstrate the effectiveness of our model and proposed modules. Moreover, our robustness experiments show that our method effectively handles data corruption during storage and transmission, exhibiting excellent stability and robustness. Our approach aims to advance automated surgical workflow recognition, addressing the complexities and dynamism inherent in surgical procedures.