Full-Reference Image Quality Assessment (FR-IQA) algorithms excel in evaluating perceptual distortions by comparing reference and distorted images. However, as the severity and quantity of distortions in datasets increase, existing FR-IQA methods struggle to capture complex nonlinear perceptual features. This limitation results in reduced adaptability and inaccurate assessments for images with more severe or multiple distortions. Recognizing the importance of understanding image degradation mechanisms, we propose a novel hierarchical degradation-aware network (HDaN) method. First, by exploring the degradation mechanisms from the reference image to the distorted image, our degradation network matches distortions that align more closely with the human visual system (HVS). Next, we design a convertor to project the matched features into multiple spaces, creating multidimensional feature representations that more comprehensively capture the complexity of image distortions rather than being confined to a single feature space. Then, we calculate a similarity matrix between the distorted and mapped features, selecting the most similar (top-k) features for merging. Finally, a regression network maps the merged features to quality scores, providing the final quality prediction. The experimental results demonstrate that our proposed HDaN method outperforms traditional deep learning-based FR-IQA methods. Specifically, the HDaN shows higher PLCC and SROCC metrics on benchmark datasets, significantly improving over existing methods. Moreover, the method exhibits better adaptability to images with varying degrees and types of distortions, thereby greatly enhancing the overall performance of IQA.