Single nucleotide polymorphisms (SNPs) are a prime source of genetic diversity. Discriminating between different SNPs provides an enormous leap towards the better understanding of the uniqueness of biological systems. Here we report on a new approach for SNP discrimination using toehold-mediated DNA strand displacement. The distinctiveness of the approach is based on the combination of both 3- and 4-way branch migration mechanisms, which allows for reliable discrimination of SNPs within double-stranded DNA generated from real-life human mitochondrial DNA samples. Aside from the potential diagnostic value, the current study represents an additional way to control the strand displacement reaction rate without altering other reaction parameters and provides new insights into the influence of single nucleotide substitutions on 3- and 4-way branch migration efficiency and kinetics.