Image classification is a typical computer vision task widely used in practical applications. The images used for training image classification networks are often clean, i.e., without any image degradation. However, Convolutional neural networks trained on clean images perform poorly on degraded or corrupted images in the real world. In this study, we effectively utilize robust data augmentation (DA) with knowledge distillation to improve the classification performance of degraded images. We first categorize robust data augmentations into geometric-and-color and cut-and-delete DAs. Next, we evaluate the effectual positioning of cut-and-delete DA when we apply knowledge distillation. Moreover, we also experimentally demonstrate that combining the RandAugment and Random Erasing approach for geometric-and-color and cut-and-delete DA improves the generalization of the student network during the knowledge transfer for the classification of degraded images.