This study implements a feature extraction based on piecewise linear Morse theory to solve the problems of incomplete feature recognition in traditional surface feature extraction algorithms, complex topological relationship construction, and difficulty in topological simplification. In addition, it proposes a new feature importance measurement index for topological simplification. Firstly, critical points are identified to form critical lines, which generates Morse-Smale complex to complete the construction of surface topological features. Thereafter, a new feature importance metric is proposed using the average eigenvalue of Morse-Smale complex to backcalculate the eigenvalues of critical points, making a double evaluation of the feature importance of this complex. Finally, the simplification and the expression of the topological features of the surface are realized based on the metric. The experimental results show that the surface features are extracted and a good topology structure is constructed. The feature extraction point cloud compression rate reaches 36.29%, and the topology simplified point cloud compression rate reaches 70.73%. This considerably reduces the massive point cloud data and eliminates redundant topology, laying a good data foundation for the subsequent expression and the application of surface point clouds.