In the domain of non-generative visual counterfactual explanations (CE), traditional techniques frequently involve the substitution of sections within a query image with corresponding sections from distractor images. Such methods have historically overlooked the semantic relevance of the replacement regions to the target object, thereby impairing the model's interpretability and hindering the editing workflow. Addressing these challenges, the present study introduces an innovative methodology named as Weighted Semantic Map with Auto-adaptive Candidate Editing Network (WSAE-Net). Characterized by two significant advancements: the determination of an weighted semantic map and the auto-adaptive candidate editing sequence. First, the generation of the weighted semantic map is designed to maximize the reduction of non-semantic feature units that need to be computed, thereby optimizing computational efficiency. Second, the auto-adaptive candidate editing sequences are designed to determine the optimal computational order among the feature units to be processed, thereby ensuring the efficient generation of counterfactuals while maintaining the semantic relevance of the replacement feature units to the target object. Through comprehensive experimentation, our methodology demonstrates superior performance, contributing to a more lucid and in-depth understanding of visual counterfactual explanations.