Enabling autonomous robots to safely and efficiently navigate, explore, and map underwater caves is of significant importance to water resource management, hydrogeology, archaeology, and marine robotics. In this work, we demonstrate the system design and algorithmic integration of a visual servoing framework for semantically guided autonomous underwater cave exploration. We present the hardware and edge-AI design considerations to deploy this framework on a novel AUV (Autonomous Underwater Vehicle) named CavePI. The guided navigation is driven by a computationally light yet robust deep visual perception module, delivering a rich semantic understanding of the environment. Subsequently, a robust control mechanism enables CavePI to track the semantic guides and navigate within complex cave structures. We evaluate the system through field experiments in natural underwater caves and spring-water sites and further validate its ROS (Robot Operating System)-based digital twin in a simulation environment. Our results highlight how these integrated design choices facilitate reliable navigation under feature-deprived, GPS-denied, and low-visibility conditions.