The Segment Anything Model (SAM) exhibits a capability to segment a wide array of objects in natural images, serving as a versatile perceptual tool for various downstream image segmentation tasks. In contrast, medical image segmentation tasks often rely on domain-specific knowledge (DSK). In this paper, we propose a novel method (SamDSK) that combines the segmentation foundation model (i.e., SAM) with domain-specific knowledge (DSK) for reliable utilization of unlabeled images in building a medical image segmentation model. Our new method is iterative and consists of two main stages: (1) segmentation model training; (2) expanding the labeled set by using the trained segmentation model, an unlabeled set, SAM, and domain-specific knowledge. These two stages are repeated until no more samples are added to the labeled set. A novel optimal-matching-based method is developed for combining the SAM-generated segmentation proposals and pixel-level and image-level DSK for constructing annotations of unlabeled images in the iterative stage (2). In experiments, we demonstrate the effectiveness of our proposed method for breast cancer segmentation in ultrasound images, polyp segmentation in endoscopic images, and skin lesion segmentation in dermoscopic images. The code is available at github.com/yizhezhang2000/SamDSK.