Medical image segmentation and video object segmentation are essential for diagnosing and analyzing diseases by identifying and measuring biological structures. Recent advances in natural domain have been driven by foundation models like the Segment Anything Model 2 (SAM-2). To explore the performance of SAM-2 in biomedical applications, we designed three evaluation pipelines for single-frame 2D image segmentation, multi-frame 3D image segmentation and multi-frame video segmentation with varied prompt designs, revealing SAM-2's limitations in medical contexts. Consequently, we developed BioSAM-2, an enhanced foundation model optimized for biomedical data based on SAM-2. Our experiments show that BioSAM-2 not only surpasses the performance of existing state-of-the-art foundation models but also matches or even exceeds specialist models, demonstrating its efficacy and potential in the medical domain.