Population genetic models predict that populations that are geographically close to each other are expected to be genetically more similar to each other compared to those that are widely separate. However the patterns of relationships between geographic distance and molecular divergences at neutral and constrained regions of the genome are unclear. We attempted to clarify this relationship by sequencing complete mitochondrial genomes of the relic species Tuatara (Sphenodon punctatus) from ten offshore islands of New Zealand. We observed a positive relationship that showed a proportional increase in the neutral diversity at synonymous sites (dS), with increasing geographical distance. In contrast we showed that diversity at evolutionarily constrained sites (dC) was elevated in the case of comparisons involving closely located populations. Conversely diversity was reduced in the case of comparisons between distantly located populations. These patterns were confirmed by a significant negative relationship between the ratio of dC/dS and geographic distance. The observed high dC/dS could be explained by the abundance of deleterious mutations in comparisons involving closely located populations, due to the recent population divergence times. Since distantly related populations were separated over long periods of time, deleterious mutations might have been removed by purifying selection.