For building a reliable spoof detection system for speaker verification applications, it is important to ensure that the system generalizes well to spoof attack types 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 a novel two-stage mixup strategies which are designed to increase the generalization 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 dataset, and the proposed framework showed the best performance.