Modeling complementary relationships greatly helps recommender systems to accurately and promptly recommend the subsequent items when one item is purchased. Unlike traditional similar relationships, items with complementary relationships may be purchased successively (such as iPhone and Airpods Pro), and they not only share relevance but also exhibit dissimilarity. Since the two attributes are opposites, modeling complementary relationships is challenging. Previous attempts to exploit these relationships have either ignored or oversimplified the dissimilarity attribute, resulting in ineffective modeling and an inability to balance the two attributes. Since Graph Neural Networks (GNNs) can capture the relevance and dissimilarity between nodes in the spectral domain, we can leverage spectral-based GNNs to effectively understand and model complementary relationships. In this study, we present a novel approach called Spectral-based Complementary Graph Neural Networks (SComGNN) that utilizes the spectral properties of complementary item graphs. We make the first observation that complementary relationships consist of low-frequency and mid-frequency components, corresponding to the relevance and dissimilarity attributes, respectively. Based on this spectral observation, we design spectral graph convolutional networks with low-pass and mid-pass filters to capture the low-frequency and mid-frequency components. Additionally, we propose a two-stage attention mechanism to adaptively integrate and balance the two attributes. Experimental results on four e-commerce datasets demonstrate the effectiveness of our model, with SComGNN significantly outperforming existing baseline models.