The 2280 km long Jinsha River has been blocked at least four times in the past 30 years. A landslide damming hazard chain can endanger communities and infrastructures hundreds of kilometers downstream from the damming site in alpine gorges. Past damming events have resulted in severe consequences, demanding a thorough assessment of damming threats along the entire Jinsha River. This study digitizes the Jinsha River and visualizes its topographic, tectonic, hydrologic, and climate characteristics in detail. A two-stage full-probability method is proposed for assessing the damming threats along this river, making it possible to identify potential damming hotspots and high-priority zones for hazard mitigation. It is found that the upper reach of the Jinsha River poses the greatest damming threat, and the threat level gradually decreases downstream. Approximately 33.4%, 36.7%, 20.5%, and 9.4% of the entire length of the Jinsha River are classified as low, moderate, high, and very high threat levels, respectively. Compared with existing hydropower projects, future projects in the upper reach are more likely to be exposed to landslide damming. We highlight the value of basin-scale spatial threat analysis and envisage that our findings will promote more targeted local-scale risk assessments for potential damming hotspots. These outcomes provide the basis for managing the risks of river damming and hydropower infrastructure along the Jinsha River.