Large mitochondrial DNA fragments and nearly complete mitogenomes were obtained from nextera-tagmented reductively amplified DNA (nextRAD) data from the Rio Grande silvery minnow (Hybognathus amarus). We used these data to characterize variation across the mitogenome and to evaluate changes in mitochondrial diversity across a 20 year time series punctuated by marked species decline. We observed different evolutionary rates among protein-coding genes and inflated values of the ratio of non-synonymous change to non-synonymous sites to synonymous changes per synonymous site for several protein-coding genes, violating assumptions of selective neutrality. Analyses suggested that non-synonymous substitutions are effectively neutral, and our results were not consistent with genetic draft. Mitogenomes revealed large long-term effective population size for Rio Grande silvery minnow, and time-series data indicated recent reductions in mitochondrial diversity via genetic drift associated with population bottlenecks. The results presented in this study show that in some cases, nextRAD sequences contain informative mitochondrial DNA data.