Open-vocabulary part segmentation (OVPS) is an emerging research area focused on segmenting fine-grained entities based on diverse and previously unseen vocabularies.Our study highlights the inherent complexities of part segmentation due to intricate boundaries and diverse granularity, reflecting the knowledge-based nature of part identification.To address these challenges, we propose PartCLIPSeg, a novel framework utilizing generalized parts and object-level contexts to mitigate the lack of generalization in fine-grained parts.PartCLIPSeg integrates competitive part relationships and attention control techniques, alleviating ambiguous boundaries and underrepresented parts.Experimental results demonstrate that PartCLIPSeg outperforms existing state-of-the-art OVPS methods, offering refined segmentation and an advanced understanding of part relationships in images.Through extensive experiments, our model demonstrated an improvement over the state-of-the-art models on the Pascal-Part-116, ADE20K-Part-234, and PartImageNet datasets.Our code will be available at https://anonymous.4open.science/r/part-clipseg-A526