Segment Anything Model (SAM) struggles with segmenting objects in the open world, especially across diverse and dynamic domains. Continual segmentation (CS) is a potential technique to solve this issue, but a significant obstacle is the intractable balance between previous domains (stability) and new domains (plasticity) during CS. Furthermore, how to utilize two kinds of features of SAM, images and prompts, in an efficient and effective CS manner remains a significant hurdle. In this work, we propose a novel CS method, termed SAMCL, to address these challenges. It is the first study to empower SAM with the CS ability across dynamic domains. SAMCL decouples stability and plasticity during CS by two components: $\textit{AugModule}$ and $\textit{Module Selector}$. Specifically, SAMCL leverages individual $\textit{AugModule}$ to effectively and efficiently learn new relationships between images and prompts in each domain. $\textit{Module Selector}$ selects the appropriate module during testing, based on the inherent ability of SAM to distinguish between different domains. These two components enable SAMCL to realize a task-agnostic method without any interference across different domains. Experimental results demonstrate that SAMCL outperforms state-of-the-art methods, achieving an exceptionally low average forgetting of just $0.5$%, along with at least a $2.5$% improvement in transferring to unseen domains. Moreover, the tunable parameter consumption in AugModule is about $0.236$MB, marking at least a $23.3$% reduction compared to other fine-tuning methods.