Digital Elevation Model (DEM)-based mountain vertex extraction is one of the most useful DEM applications, providing important information to properly characterize topographic features. Current vertex-extraction techniques have considerable limitations, such as yielding low-accuracy results and generating false mountain vertices. To overcome these limitations, a new approach is proposed that combines Hotspot Analysis Clustering and the Improved Eight-Connected Extraction algorithms that would quickly and accurately provide the location and elevation of mountain vertices. The use of the elevation-based Hotspot Analysis Clustering Algorithm allows the fast partitioning of the mountain vertex area, which significantly reduces data and considerably improves the efficiency of mountain vertex extraction. The algorithm also minimizes false mountain vertices, which can be problematic in valleys, ridges, and other rugged terrains. The Eight-Connected Extraction Algorithm also hastens the precise determination of vertex location and elevation, providing a better balance between accuracy and efficiency in vertex extraction. The proposed approach was used and tested on seven different datasets and was compared against traditional vertex extraction methods. The results of the quantitative evaluation show that the proposed approach yielded higher efficiency, considerably minimized the occurrence of invalid points, and generated higher vertex extraction accuracy compared to other traditional methods.