MOTIVATION: Embryo selection is one of the critical factors in determining the success of pregnancy in in vitro fertilization procedures. Using artificial intelligence to aid in embryo selection could effectively address the current time-consuming, expensive, subjectively influenced process of embryo assessment by trained embryologists. However, current deep learning-based methods often focus on blastocyst segmentation, grading, or predicting cell development via time-lapse videos, often overlooking morphokinetic parameters or lacking interpretability. Given the significance of both morphokinetic and morphological evaluation in predicting the implantation potential of cleavage-stage embryos, as emphasized by previous research, there is a necessity for an automated method to segment cleavage-stage embryos to improve this process. RESULTS: In this article, we introduce the SAM-based dual branch segmentation pipeline for automated segmentation of blastomeres in cleavage-stage embryos. Leveraging the powerful segmentation capability of SAM, the instance branch conducts instance segmentation of blastomeres, while the semantic branch performs semantic segmentation of fragments. Due to the lack of publicly available datasets, we construct the CleavageEmbryo dataset, the first dataset of human cleavage-stage embryos with pixel-level annotations containing fragment information. We train and test a series of state-of-the-art segmentation algorithms on CleavageEmbryo. Our experiments demonstrate that our method outperforms existing algorithms in terms of objective metrics (mAP 0.874 on blastomeres, Dice 0.695 on fragments) and visual quality, enabling more accurate segmentation of cleavage-stage embryos. AVAILABILITY AND IMPLEMENTATION: The code and sample data in this study can be found at: https://github.com/12austincc/Cleavage-StageEmbryoSegmentation.