The segmentation of dermoscopic images is a crucial phase in computer-aided diagnostic systems. Dermoscopic images are often affected by artifacts and noise. Also, many images have unclear boundaries between lesion and background pixels. Hence, under such conditions, the segmentation of dermoscopic images becomes challenging. To overcome these challenges, we introduce a novel image segmentation method in the neutrosophic set framework with local spatial information (NCM_S) for dermoscopic images. The neutrosophic set-based approach used in the proposed NCM_Sgives a more nuanced representation of the image pixels, effectively addressing the vagueness present due to unclear boundaries. Incorporating local spatial information into the objective function of traditional neutrosophic c-means makes the proposed NCM_Smethod less sensitive to artifacts and noise. We demonstrate the effectiveness of the proposed NCM_Smethod on two publicly available datasets. We compare the performance of NCM_Swith six existing non-fuzzy-based clustering methods for skin-lesion segmentation and eight fuzzy-based clustering methods in terms of Dice score and Jaccard index. The results of the experiments indicate that the proposed NCM_Smethod is superior to the six skin-lesion segmentation and eight fuzzy-based clustering methods.