Since pathological images have some distinct characteristics that are different from natural images, the direct application of a general convolutional neural network cannot achieve good classification performance, especially for fine-grained classification problems (such as pathological image grading). Inspired by the clinical experience that decomposing a pathological image into different components is beneficial for diagnosis, in this paper, we propose a ivide-and-ttention work () for Hematoxylin-and-Eosin (HE)-stained pathological image classification. The DANet utilizes a deep-learning method to decompose a pathological image into nuclei and non-nuclei parts. With such decomposed pathological images, the DANet first performs feature learning independently in each branch, and then focuses on the most important feature representation through the branch selection attention module. In this way, the DANet can learn representative features with respect to different tissue structures and adaptively focus on the most important ones, thereby improving classification performance. In addition, we introduce deep canonical correlation analysis (DCCA) constraints in the feature fusion process of different branches. The DCCA constraints play the role of branch fusion attention, so as to maximize the correlation of different branches and ensure that the fused branches emphasize specific tissue structures. The experimental results of three datasets demonstrate the superiority of the DANet, with an average classification accuracy of 92.5% on breast cancer classification, 95.33% on colorectal cancer grading, and 91.6% on breast cancer grading tasks.