Graph-structured datasets usually have irregular graph sizes and connectivities, rendering the use of recent data augmentation techniques, such as Mixup, difficult. To tackle this challenge, we present the first Mixup-like graph augmentation method called Graph Transplant, which mixes irregular graphs in data space. To be well defined on various scales of the graph, our method identifies the sub-structure as a mix unit that can preserve the local information. Since the mixup-based methods without special consideration of the context are prone to generate noisy samples, our method explicitly employs the node saliency information to select meaningful subgraphs and adaptively determine the labels. We extensively validate our method with diverse GNN architectures on multiple graph classification benchmark datasets from a wide range of graph domains of different sizes. Experimental results show the consistent superiority of our method over other basic data augmentation baselines. We also demonstrate that Graph Transplant enhances the performance in terms of robustness and model calibration.