Tag-aware recommendation algorithms use tagged data to enhance the recommendation models’ understanding of user preferences and item attributes, which attract extensive attention in the field. Most existing methods, however, neglect the diversities of user concerns, item attributes, and tag semantics and interfere with the correlation inference of the three, which affects the recommendation results. Therefore, this paper introduces the disentangled graph collaborative filtering (DGCF) method into the tag-aware recommendation task and proposes a DGCF-based explainable tag-aware recommendation (DETRec) method. It disentangles the perspectives of users, items, and tags to provide explainable recommendation references. Specifically, DETRec utilizes a correlation graph construction module to model the user–item–tag correlations. Then, it employs a neighborhood routing mechanism and a message propagation mechanism to disentangle the nodes to form the sub-graphs of attributes and thereby describe the nodal correlations under different attributes. Finally, it generates recommendation references on the basis of these attribute sub-graphs. This study implements two types of DETRec instantiation: 1) DETRec based on a single graph (DETRec-S), which describes all correlations of user, item, and tag nodes in a single graph, and 2) DETRec based on multiple graphs (DETRec-M), which utilizes three bipartite graphs to describe the user–item, item–tag, and user–tag correlations separately. Extensive experiments on three public datasets demonstrate that the above two types of DETRec instantiation are significantly superior to the baseline model and generate the references corresponding to the recommendation results. Hence, DETRec is an effective explainable tag-aware recommendation algorithm.