Graph Neural Networks (GNNs) have recently been widely adopted in multiple domains. Yet, they are notably vulnerable to adversarial and backdoor attacks. In particular, backdoor attacks based on subgraph insertion have been shown to be effective in graph classification tasks while being stealthy, successfully circumventing various existing defense methods. In this paper, we propose E-SAGE, a novel approach to defending GNN backdoor attacks based on explainability. We find that the malicious edges and benign edges have significant differences in the importance scores for explainability evaluation. Accordingly, E-SAGE adaptively applies an iterative edge pruning process on the graph based on the edge scores. Through extensive experiments, we demonstrate the effectiveness of E-SAGE against state-of-the-art graph backdoor attacks in different attack settings. In addition, we investigate the effectiveness of E-SAGE against adversarial attacks.