The main objective of the spoof detection system for speaker verification applications is to capture the artifacts from the given speech sample. Therefore, it is important to ensure that the countermeasure system generalizes well to spoof artifact patterns unobserved during the training process. To achieve this, we explore various possible adaptations of the mixup augmentation technique to the spoof detection system training, which involves mixing within-bonafide, within-spoof, and between bonafide and spoof samples. Moreover, we propose novel two-stage mixup strategies which are designed to increase the generalization power of the end-to-end spoof detection system to unseen attack types. The systems trained with different mixup configurations were experimented on the logical access (LA) task of the ASVSpoof2019 challenge dataset, and the proposed framework showed the best performance.