Graph (structure) augmentation aims to perturb the graph structure through heuristic or probabilistic rules, enabling the nodes to capture richer contextual information and thus improving generalization performance. While there have been a few graph structure augmentation methods proposed recently, none of them are aware of a potential negative augmentation problem, which may be caused by overly severe distribution shifts between the original and augmented graphs. In this paper, we take an important graph property, namely graph homophily, to analyze the distribution shifts between the two graphs and thus measure the severity of an augmentation algorithm suffering from negative augmentation. To tackle this problem, we propose a novel Knowledge Distillation for Graph Augmentation (KDGA) framework, which helps to reduce the potential negative effects of distribution shifts, i.e., negative augmentation problem. Specifically, KDGA extracts the knowledge of any GNN teacher model trained on the augmented graphs and injects it into a partially parameter-shared student model that is tested on the original graph. As a simple but efficient framework, KDGA is applicable to a variety of existing graph augmentation methods and can significantly improve the performance of various GNN architectures. For three popular graph augmentation methods, namely GAUG, MH-Aug, and GraphAug, the experimental results show that the learned student models outperform their vanilla implementations by an average accuracy of 4.6% (GAUG), 4.2% (MH-Aug), and 4.6% (GraphAug) on eight graph datasets.