Task-oriented grasping, which involves grasping specific parts of objects based on their functions, is crucial for developing advanced robotic systems capable of performing complex tasks in dynamic environments. In this paper, we propose a training-free framework that incorporates both semantic and geometric priors for zero-shot task-oriented grasp generation. The proposed framework, SegGrasp, first leverages the vision-language models like GLIP for coarse segmentation. It then uses detailed geometric information from convex decomposition to improve segmentation quality through a fusion policy named GeoFusion. An effective grasp pose can be generated by a grasping network with improved segmentation. We conducted the experiments on both segmentation benchmark and real-world robot grasping. The experimental results show that SegGrasp surpasses the baseline by more than 15\% in grasp and segmentation performance.