Graph neural networks (GNNs) have achieved state-of-the-art performance in many graph learning tasks. However, recent studies show that GNNs are vulnerable to both test-time evasion and training-time poisoning attacks that perturb the graph structure. While existing attack methods have shown promising attack performance, we would like to design an attack framework to further enhance the performance. In particular, our attack framework is inspired by certified robustness, which was originally used by defenders to defend against adversarial attacks. We are the first, from the attacker perspective, to leverage its properties to better attack GNNs. Specifically, we first derive nodes' certified perturbation sizes against graph evasion and poisoning attacks based on randomized smoothing, respectively. A larger certified perturbation size of a node indicates this node is theoretically more robust to graph perturbations. Such a property motivates us to focus more on nodes with smaller certified perturbation sizes, as they are easier to be attacked after graph perturbations. Accordingly, we design a certified robustness inspired attack loss, when incorporated into (any) existing attacks, produces our certified robustness inspired attack counterpart. We apply our framework to the existing attacks and results show it can significantly enhance the existing base attacks' performance.