: Slope instability is a common geological hazard in open-pit mines, which may cause huge economic losses and casualties. Thus, it is important to cluster and evaluate the stability of slopes effectively. This article proposes a hyperbolic sine similarity measure of single-valued neutrosophic sets (SVNSs) for a netting clustering method and a slope stability evaluation method to cluster and assess the stability of open-pit mine slopes. This study contains the following main content. First, we present a hyperbolic sine similarity measure between SVNSs. Second, slope stability impact factors are fuzzified into SVNSs by the utilization of true, indeterminate, and false membership functions, and then a netting clustering method using the proposed similarity measure is proposed to cluster the stability of open-pit mine slopes. Third, we propose a slope stability evaluation method based on the proposed similarity measure, where we give the SVNS knowledge of risk grades/patterns based on the clustering results of slope stability and then present the similarity measure values between the risk grades/patterns and the slope samples to assess that each slope sample with the larger measure value belongs to the corresponding slope risk grade. Finally, the proposed netting clustering and evaluation methods are applied to the clustering analysis and assessment of 20 open-pit mine slope samples to verify the rationality and effectivity of the proposed approaches in the scenario of SVNSs.