Deep learning approaches are widely applied to histopathological image analysis due to the impressive levels of performance achieved. However, when dealing with high-resolution histopathological images, utilizing the original image as input to the deep learning model is computationally expensive, while resizing the original image to achieve low resolution incurs information loss. Some hard-attention based approaches have emerged to select possible lesion regions from images to avoid processing the original image. However, these hard-attention based approaches usually take a long time to converge with weak guidance, and valueless patches may be trained by the classifier. To overcome this problem, we propose a deep selective attention approach that aims to select valuable regions in the original images for classification. In our approach, a decision network is developed to decide where to crop and whether the cropped patch is necessary for classification. These selected patches are then trained by the classification network, which then provides feedback to the decision network to update its selection policy. With such a co-evolution training strategy, we show that our approach can achieve a fast convergence rate and high classification accuracy. Our approach is evaluated on a public breast cancer histopathological image database, where it demonstrates superior performance compared to state-of-the-art deep learning approaches, achieving approximately 98% classification accuracy while only taking 50% of the training time of the previous hard-attention approach.