Single-point annotation in visual tasks, with the goal of minimizing labelling costs, is becoming increasingly prominent in research. Recently, visual foundation models, such as Segment Anything (SAM), have gained widespread usage due to their robust zero-shot capabilities and exceptional annotation performance. However, SAM's class-agnostic output and high confidence in local segmentation introduce 'semantic ambiguity', posing a challenge for precise category-specific segmentation. In this paper, we introduce a cost-effective category-specific segmenter using SAM. To tackle this challenge, we have devised a Semantic-Aware Instance Segmentation Network (SAPNet) that integrates Multiple Instance Learning (MIL) with matching capability and SAM with point prompts. SAPNet strategically selects the most representative mask proposals generated by SAM to supervise segmentation, with a specific focus on object category information. Moreover, we introduce the Point Distance Guidance and Box Mining Strategy to mitigate inherent challenges: 'group' and 'local' issues in weakly supervised segmentation. These strategies serve to further enhance the overall segmentation performance. The experimental results on Pascal VOC and COCO demonstrate the promising performance of our proposed SAPNet, emphasizing its semantic matching capabilities and its potential to advance point-prompted instance segmentation. The code are available at https://github.com/CVPR666/SAPNet.