Generalized zero-shot semantic segmentation (GZS3) aims to achieve the human-level capability of segmenting not only seen classes but also novel class regions unseen in the training data through introducing the bridge of semantic representations, e.g., word vector. While effective, the way of utilizing one semantic representation to associate the corresponding class and to enable the knowledge transfer from seen to unseen classes is insufficient as well as incompatible with human cognition. Inspired by the observation that humans often use some `part' and `state' information to comprehend the seen objects and imagine unseen classes, we decouple each class into detailed descriptions, including object parts and states. Based on the decoupling formulation, we propose a Decoupled Vision-Language Matching (DeVLMatch) framework, composed of spatial-part (SPMatch) and channel-state (CSMatch) matching modules, for GZS3. In SPMatch, we comprehend objects with spatial part information from both visual and linguistic perspectives and perform graph matching to bridge the gap. In CSMatch, states of objects from the linguistic perspective are matched to compatible channel information from the visual perspective. By decoupling and matching objects across visual and linguistic comprehension, we can explicitly introspect the relationship between seen and unseen classes in fine-grained object part and state levels, thereby facilitating the knowledge transfer from seen to unseen classes in visual space. The proposed DeVLMatch framework surpasses the previous GZS3 methods on standard benchmarks, including PASCAL VOC, COCO-Stuff, and CATARACTS, demonstrating its effectiveness.