Student communication during collaborative problem solving centers on sharing and negotiating ideas, regulating problem-solving processes, and maintaining social interaction. These cognitively and socially driven processes help students consolidate knowledge, manage their actions, and engage effectively in collaborative learning environments. To enhance these environments, analyzing student dialogue is crucial for delivering adaptive scaffolding and fostering deeper engagement and collaboration. However, such analysis poses significant challenges due to the complexity of student interactions and the need for interpretable analysis. To address these challenges, we introduce a novel framework for analyzing collaborative problem-solving dialogue that integrates temporal clustering of dialogue patterns with LLM-generated explanations. Using video and chat log data from middle school student groups engaged in a collaborative game-based learning environment, we demonstrate that our framework effectively identifies collaborative problem-solving dialogue patterns. Furthermore, the LLM-generated interpretations enhance the interpretability of these clusters, to enable both collaborative problem-solving assessment and early prediction of learning outcomes. This work lays the foundation for enabling adaptive scaffolding, automated collaboration assessment, and improved learning processes within collaborative, game-based educational settings.