•A BIM and knowledge graph-based framework for automatic model auditing and QTO.•A data model and mechanisms to obtain graph representations and embeddings from BIM.•An improved transR model to obtain better knowledge graph embeddings.•A self-evolving mechanism to automatically determine mistake elements.•100% sensitivity and 94% specificity on average in testing BIM models. Model auditing is a critical step before conducting Building Information Modeling (BIM)-based Quantity Take-off (QTO) because these models may contain various human errors and mistakes, leading to insufficient semantic information and inconsistent modeling style in BIM models. The traditional object-oriented approach has difficulties in representing unstructured BIM data (e.g., interrelationships), while rule-based methods involve tremendous human efforts to develop rule sets, lacking flexibility for different requirements. Therefore, this study aims to establish a novel data-driven framework based on BIM and knowledge graph (KG) to represent unstructured BIM data for automatic inferences of auditing results of BIM model mistakes. It starts by establishing a BIM-KG data model via identifying required information for auditing purposes. Subsequently, BIM data is automatically transformed into the BIM-KG representations, the embeddings of which are trained using a knowledge graph embedding model. Automatic mechanisms are then developed to utilize the computable embeddings to effectively identify mistake BIM elements. The framework is validated using illustrative examples and the results show that 100% mistake elements can be identified successfully without human intervention.