Graph neural networks (GNNs) have achieved tremendous success in the task of graph classification and its diverse downstream real-world applications. Despite the huge success in learning graph representations, current GNN models have demonstrated their vulnerability to potentially existent adversarial examples on graph-structured data. Existing approaches are either limited to structure attacks or restricted to local information, urging for the design of a more general attack framework on graph classification, which faces significant challenges due to the complexity of generating local-node-level adversarial examples using the global-graph-level information. To address this "global-to-local" attack challenge, we present a novel and general framework to generate adversarial examples via manipulating graph structure and node features. Specifically, we make use of Graph Class Activation Mapping and its variant to produce node-level importance corresponding to the graph classification task. Then through a heuristic design of algorithms, we can perform both feature and structure attacks under unnoticeable perturbation budgets with the help of both node-level and subgraph-level importance. Experiments towards attacking four state-of-the-art graph classification models on six real-world benchmarks verify the flexibility and effectiveness of our framework.