Automatic coronary artery (CA) segmentation on coronary-computed tomography angiography (CCTA) images is critical for coronary-related disease diagnosis and pre-operative planning. However, such segmentation remains a challenging task due to the difficulty in maintaining the topological consistency of CA, interference from irrelevant tubular structures, and insufficient labeled data. In this study, we propose a novel semi-supervised topology-oriented foreground focusing network (TOFF-Net) to comprehensively address such challenges. Specifically, we first propose an explicit vascular connectivity preservation (VCP) loss to capture the topological information and effectively strengthen vascular connectivity. Then, we propose an irrelevant vessels removal (IVR) module, which aims to integrate local CA details and global CA distribution, thereby eliminating interference of irrelevant vessels. Moreover, we propose a foreground label migration and focusing (FLMF) module with Pioneer-Imitator learning as a semi-supervised strategy to exploit the unlabeled data. The FLMF can effectively guide the attention of TOFF-Net to the foreground. Extensive results on our in-house dataset and two public datasets demonstrate that our TOFF-Net achieves state-of-the-art CA segmentation performance with high topological consistency and few false-positive irrelevant tubular structures. The results also reveal that our TOFF-Net presents considerable potential for parsing other types of vessels.