Graph Neural Networks (GNNs), as promising deep learning approaches, have been applied in various areas. However, it is also known that they are vulnerable to adversarial attacks, which raises many concerns in real application. Regarding Graph Structure Attacks (GSAs), though existing homophily-based truncation defenses have showed strong defense capacity, they suffer the problem of losing much effective neighborhood information in the process of removing adversarial edges, causing a limited performance on both clean and attacked graphs. In this paper, we consider the question: Can we capture more effective neighborhood information by utilizing the higher-order network to help improve the performance of the homophily-based truncation defense? To answer it, we first explore the impacts of different GSAs on the 1-hop and 2-hop networks. We theoretically and empirically find that the 2-hop network also has a strong information retention capacity like the 1-hop network after many GSAs. Motivated by this, we combine the 2-hop network with the homophily-based truncation defense, constructing a stronger defender, MHR-GCN. It integrates effective neighborhood information from both 1-hop and 2-hop networks. Extensive experiments demonstrate that MHR-GCN significantly improves the performance of the truncation defense and outperforms the state-of-the-arts under various GSA settings, especially when the graph is heavily perturbed.