Robust perception in complex underwater environments is critical for marine resource exploration, ecological monitoring, and robotic operations, yet remains challenging due to low visibility, color distortion, dynamic backgrounds, and long-term occlusions. Although foundation models such as SAM 2 demonstrate strong segmentation performance on static imagery, their lack of explicit temporal modeling limits reliability in underwater video scenarios. To address this limitation, we propose AquaSlot-SAM, a hybrid object-centric temporal segmentation framework that integrates Slot-based State Space Models (SlotSSMs) with prompt-guided refinement in SAM 2. SlotSSMs explicitly maintain object-level temporal states, which are converted into adaptive prompts to guide SAM 2 toward spatially precise and temporally coherent segmentation. A sparse Slot Mixer enhances inter-object interaction, while confidence-aware mask fusion balances global stability and local boundary refinement. Extensive experiments on three public underwater benchmarks demonstrate that AquaSlot-SAM consistently outperforms strong contemporary baselines, achieving substantial improvements across multiple metrics and validating the effectiveness of structured memory-guided prompting for dynamic underwater segmentation.