Conversational recommender systems (CRS) enable traditional recommender systems to interact with users by asking questions about their preferences and recommending items. Conversation recommendation has made significant progress, however, studies on attribute-aware conversational recommendation have overlooked the problem that after obtaining the candidate attribute set, the relevance of the attributes in the candidate attribute set to the user’s current preferred attributes is not further considered, resulting in the existence of many user-uninterested attributes in the candidate attribute set. This seriously affects the dialogue quality and reduces the user’s patience, decreasing recommendation accuracy. To address this problem, this paper proposes a new framework called Attribute Clipping based on Dynamic Graph (ACDG). In ACDG, firstly, the reasoning module uses the restriction property of graph structure to obtain a large set of candidate attributes, and then the attribute clipping module filters out the attributes with high relevance to the current user’s preferred attributes. Thus, ACDG can obtain a better-quality set of candidate attributes. Through extensive experiments on four benchmark CRS datasets, we validate the effectiveness of the method.