While protein–nucleic acid interactions are pivotal for many crucial biological processes, limited experimental data has made the development of computational approaches to characterise these interactions a challenge. Consequently, most approaches to understand the effects of missense mutations on protein-nucleic acid affinity have focused on single-point mutations and have presented a limited performance on independent data sets. To overcome this, we have curated the largest dataset of experimentally measured effects of mutations on nucleic acid binding affinity to date, encompassing 856 single-point mutations and 141 multiple-point mutations across 155 experimentally solved complexes. This was used in combination with an optimized version of our graph-based signatures to develop mmCSM-NA (http://biosig.unimelb.edu.au/mmcsm_na), the first scalable method capable of quantitatively and accurately predicting the effects of multiple-point mutations on nucleic acid binding affinities. mmCSM-NA obtained a Pearson’s correlation of up to 0.66 (RMSE of 0.88 Kcal/mol) on single-point mutations under cross-validation, and up to 0.61 on independent non-redundant datasets of multiple-point mutations (RMSE of 1.14 Kcal/mol), outperforming similar tools. mmCSM-NA is freely available as an easy-to-use web server and API. We believe it will be an invaluable tool to shed light on the role of mutations affecting protein–nucleic acid interactions in diseases.