Classification networks of degraded images need to deal with various strengths of degradation, referred to as degradation levels, in practical applications. However, there has been limited exploration of data augmentation techniques for degraded images with various degradation levels. We propose a data augmentation technique to apply distinct data augmentations to both clean and degraded image domains. Specifically, the proposed method uses random erasing and CutBlur data augmentations for a clean and degraded image, respectively. Experimental results show that the proposed method can effectively train a classification network of degraded images without losing the classification ability of clean images. Furthermore, the results also confirm the proposed method's efficacy across various degradations, multiple network architectures, and several datasets.