In recent years, Chinese Spelling Check (CSC) has been greatly improved by designing task-specific pre-training methods or introducing auxiliary tasks, which mostly solve this task in an end-to-end fashion. In this paper, we propose to decompose the CSC workflow into detection, reasoning, and searching subtasks so that the rich external knowledge about the Chinese language can be leveraged more directly and efficiently. Specifically, we design a plug-and-play detection-and-reasoning module that is compatible with existing SOTA non-autoregressive CSC models to further boost their performance. We find that the detection-and-reasoning module trained for one model can also benefit other models. We also study the primary interpretability provided by the task decomposition. Extensive experiments and detailed analyses demonstrate the effectiveness and competitiveness of the proposed module.