In most scenarios of graph-based tasks, graph neural networks (GNNs) are trained end-to-end with labeled samples. Labeling graph samples, a time-consuming and expert-dependent process, leads to huge costs. Graph data augmentations can provide a promising method to expand labeled samples cheaply. However, graph data augmentations will damage the capacity of GNNs to distinguish non-isomorphic graphs during the supervised graph representation learning process. How to utilize graph data augmentations to expand labeled samples while preserving the capacity of GNNs to distinguish non-isomorphic graphs is a challenging research problem. To address the above problem, we abstract a novel asymmetric augmented paradigm in this paper and theoretically prove that it offers a principled approach. The asymmetric augmented paradigm can preserve the capacity of GNNs to distinguish non-isomorphic graphs while utilizing augmented labeled samples to improve the generalization capacity of GNNs. To be specific, the asymmetric augmented paradigm will utilize similar yet distinct asymmetric weights to classify the real sample and augmented sample, respectively. To systemically explore the benefits of asymmetric augmented paradigm under different GNN architectures, rather than studying individual asymmetric augmented GNN (A2GNN) instance, we then develop an auto-search engine called Asymmetric Augmented Graph Neural Architecture Search (A2GNAS) to save human efforts. We empirically validate our asymmetric augmented paradigm on multiple graph classification benchmarks, and demonstrate that representative A2GNN instances automatically discovered by our A2GNAS method achieve state-of-the-art performance compared with competitive baselines. Our codes are available at: https://github.com/csubigdata-Organization/A2GNAS.