Given a graph dataset, how can we augment it for accurate graph classification? Graph augmentation is an essential strategy to improve the performance of graph-based tasks, and has been widely utilized for analyzing web and social graphs. However, previous works for graph augmentation either a) involve the target model in the process of augmentation, losing the generalizability to other tasks, or b) rely on simple heuristics that lead to unreliable results. In this work, we introduce five desired properties for effective augmentation. Then, we propose NodeSam (Node Split and Merge) and SubMix (Subgraph Mix), two model-agnostic approaches for graph augmentation that satisfy all desired properties with different motivations. NodeSam makes a balanced change of the graph structure to minimize the risk of semantic change, while SubMix mixes random subgraphs of multiple graphs to create rich soft labels combining the evidence for different classes. Our experiments on social networks and molecular graphs show that NodeSam and SubMix outperform existing approaches in graph classification.