Open-vocabulary 3D functionality segmentation enables robots to localize functional object components in 3D scenes. It is a challenging task that requires spatial understanding and task interpretation. Current open-vocabulary 3D segmentation methods primarily focus on object-level recognition, while scene-wide part segmentation methods attempt to segment the entire scene exhaustively, making them highly resource-intensive and time consuming. Balancing segmentation performance in terms of granularity, accuracy, and speed remains a challenge. As one step towards alleviating this, we introduce T-FunS3D, a task-driven hierarchical open-vocabulary 3D functionality segmentation method that provides actionable perception for robotic applications. Our method takes as input the 3D point cloud and posed RGB-D images of an indoor scene. We construct an open-vocabulary scene graph by extracting instances and their visual embeddings in the environment. Given a task description, T-FunS3D identifies the most relevant instances in the scene graph and locates their functional components leveraging a vision-language model. Experiments on the SceneFun3D dataset demonstrate that T-FunS3D is comparable to state-of-the-art in open-vocabulary 3D functionality segmentation, while achieving faster runtime and reduced memory usage.