In cognitive diagnostic models (CDMs), a set of fine-grained attributes is required to characterize complex problem solving and provide detailed diagnostic information about an examinee. However, it is challenging to ensure reliable estimation and control computational complexity when The test aims to identify the examinee's attribute profile in a large-scale map of attributes. To address this problem, this study proposes a cognitive diagnostic multistage testing by partitioning hierarchically structured attributes (CD-MST-PH) as a multistage testing for CDM. In CD-MST-PH, multiple testlets can be constructed based on separate attribute groups before testing occurs, which retains the advantages of multistage testing over fully adaptive testing or the on-the-fly approach. Moreover, testlets are offered sequentially and adaptively, thus improving test accuracy and efficiency. An item information measure is proposed to compute the discrimination power of an item for each attribute, and a module assembly method is presented to construct modules anchored at each separate attribute group. Several module selection indices for CD-MST-PH are also proposed by modifying the item selection indices used in cognitive diagnostic computerized adaptive testing. The results of simulation study show that CD-MST-PH can improve test accuracy and efficiency relative to the conventional test without adaptive stages.