Function is defined as the ensemble of tasks that enable the product to complete the designed purpose. Functional tools, such as functional modeling, offer decision guidance in the early phase of product design, where explicit design decisions are yet to be made. Function-based design data is often sparse and grounded in individual interpretation. As such, function-based design tools can benefit from automatic function classification to increase data fidelity and provide function representation models that enable function-based intelligent design agents. Function-based design data is commonly stored in manually generated design repositories. These design repositories are a collection of expert knowledge and interpretations of function in product design bounded by function-flow and component taxonomies. In this work, we represent a structured taxonomy-based design repository as assembly-flow graphs, then leverage a graph neural network (GNN) model to perform automatic function classification. We support automated function classification by learning from repository data to establish the ground truth of component function assignment. Experimental results show that our GNN model achieves a micro-average F1-score of 0.617 for tier 1 (broad), 0.624 for tier 2, and 0.415 for tier 3 (specific) functions. Given the imbalance of data features and the subjectivity in the definition of product function, the results are encouraging. Our efforts in this paper can be a starting point for more sophisticated applications in knowledge-based CAD systems and Design-for-X consideration in function-based design.