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Segment Anything Model (SAM) has demonstrated remarkable zero-shot segmentation capabilities across various visual tasks. However, its performance degrades significantly when deployed in new target domains with substantial distribution shifts. While existing self-training methods based on fixed teacher-student architectures have shown improvements, they struggle to ensure that the teacher network consistently outperforms the student under severe domain shifts. To address this limitation, we propose a novel Collaborative Mutual Learning Framework for source-free SAM adaptation, leveraging dual-networks in a dynamic and cooperative manner. Unlike fixed teacher-student paradigms, our method dynamically assigns the teacher and student roles by evaluating the reliability of each collaborative network in each training iteration. Our framework incorporates a dynamic mutual learning mechanism with three key components: a direct alignment loss for knowledge transfer, a reverse distillation loss to encourage diversity, and a triplet relationship loss to refine feature representations. These components enhance the adaptation capabilities of the collaborative networks, enabling them to generalize effectively to target domains while preserving their pre-trained knowledge. Extensive experiments on diverse target domains demonstrate that our proposed framework achieves state-of-the-art adaptation performance.