Surface-enhanced Raman spectroscopy (SERS), as a label-free, highly sensitive analytical method, has become an important tool for providing substance fingerprints. In this study, silver nanoparticles containing thiosulfate ions and calcium ions (Ag@SCNPs) have been used as an enhanced substrate to eliminate the interference of impurities on DNA signals. Intrinsic structural information on single-strand DNA (ssDNA) was directly obtained through SERS. The improved enhancement system was used to explore the base-stacking rules of ssDNA in a solution environment. For the first time, single-base insertion mutations and deletion mutations, as well as their exact mutation sites, were identified, and Raman spectra with high stability, repeatability, and high signal-to-noise ratio were obtained. The method is simple, fast, and accurate, and the detection process is nondestructive. It has potential to be applied in the fields of medical diagnosis and genetics research.