Conventional copy-paste augmentations generate new training instances by concatenating existing utterances to increase the amount of data for neural network training. However, the direct application of copy-paste augmentation for anti-spoofing is problematic. This paper refines the copy-paste augmentation for speech anti-spoofing, dubbed CpAug, to generate more training data with rich intra-class diversity. The CpAug employs two policies: concatenation to merge utterances with identical labels, and substitution to replace segments in an anchor utterance. Besides, considering the impacts of speakers and spoofing attack types, we craft four blending strategies for the CpAug. Furthermore, we explore how CpAug complements the Rawboost augmentation method. Experimental results reveal that the proposed CpAug significantly improves the performance of speech anti-spoofing. Particularly, CpAug with substitution policy leads to relative improvements of 43% and 38% on the ASVspoof’ 19LA and 21LA, respectively. Notably, the CpAug and Rawboost synergize effectively, achieving an EER of 2.91% on ASVspoof’ 21LA.