The elimination of mixed errors is a key preprocessing technology for the area of digital elevation model data analysis, which is important for further applying data. We associated group sparsity with the low-rank uniqueness of local transformations of mixing errors to effectively remove mixing errors in data from Shuttle Radar Topography Mission 1 (SRTM 1) based on the sparseness of low-rank groups. First, the stripe-error structure that appeared globally in multiple directions was able to be better represented locally using group-sparse regularization and the uniqueness of the data in the low-rank direction of the local range and using variational ideas to constrain the gradient direction of the data to avoid redundant elimination. Second, the nonlocal self-similarity of the weighted kernel norm was used to remove random noise. Finally, the proposed model for eliminating mixed errors was solved using an algorithm based on the multiplier method of alternating direction. Experiments using simulated and real data found that the proposed low-rank group-sparse method (LRGS) eliminated mixed errors in both visual and quantitative evaluations better than the most recent processing methods and existing dataset products.