Breast cancer is one of the leading cancers of women. Ultrasound is often used for breast cancer diagnosis because it is harmless, portable, and low-cost. However, the segmentation of breast ultrasound (BUS) images is a difficult task due to their low contrast and speckle noise. Neutrosophy studies the origin, nature, and scope of neutralities and their interactions with different ideational spectra. It is a new philosophy to extend fuzzy logic and is the basis of neutrosophic logic, neutrosophic probability theory, neutrosophic set theory, and neutrosophic statistics. In this paper, we employ neutrosophy and develop a fully automatic algorithm for BUS image segmentation. By using neutrosophy, we integrate two conflicting opinions about speckle in ultrasound image: speckle is noise and speckle includes pattern information. The experiments demonstrate that the proposed approach is accurate, effective, and robust.