The rise of Large Language Models (LLMs) has impacted research in robotics and automation. While progress has been made in integrating LLMs into general robotics tasks, a noticeable void persists in their adoption in more specific domains such as surgery, where critical factors such as reasoning, explainability, and safety are paramount. Achieving autonomy in robotic surgery, which entails the ability to reason and adapt to changes in the environment, remains a significant challenge. In this work, we propose a multi-modal LLM integration in robot-assisted surgery for autonomous blood suction. The reasoning and prioritization are delegated to the higher-level task-planning LLM, and the motion planning and execution are handled by the lower-level deep reinforcement learning model, creating a distributed agency between the two components. As surgical operations are highly dynamic and may encounter unforeseen circumstances, blood clots and active bleeding were introduced to influence decision-making. Results showed that using a multi-modal LLM as a higher-level reasoning unit can account for these surgical complexities to achieve a level of reasoning previously unattainable in robot-assisted surgeries. These findings demonstrate the potential of multi-modal LLMs to significantly enhance contextual understanding and decision-making in robotic-assisted surgeries, marking a step toward autonomous surgical systems.