Current research on continual learning mainly focuses on relieving catastrophic forgetting, and most of their success is at the cost of limiting the performance of newly incoming tasks. Such a trade-off is referred to as the stability-plasticity dilemma and is a more general and challenging problem for continual learning. However, the inherent conflict between these two concepts makes it seemingly impossible to devise a satisfactory solution to both of them simultaneously. Therefore, we ask, ``is it possible to divide them into two separate problems to conquer them independently?''. To this end, we propose a prompt-tuning-based method termed PromptFusion to enable the decoupling of stability and plasticity. Specifically, PromptFusion consists of a carefully designed \stab module that deals with catastrophic forgetting and a \boo module to learn new knowledge concurrently. Furthermore, to address the computational overhead brought by the additional architecture, we propose PromptFusion-Lite which improves PromptFusion by dynamically determining whether to activate both modules for each input image. Extensive experiments show that both PromptFusion and PromptFusion-Lite achieve promising results on popular continual learning datasets for class-incremental and domain-incremental settings. Especially on Split-Imagenet-R, one of the most challenging datasets for class-incremental learning, our method can exceed state-of-the-art prompt-based method CODAPrompt by more than 5\% in accuracy, with PromptFusion-Lite using 14.8\% less computational resources than PromptFusion.