Trypanosoma brucei and related parasites contain an unusual catenated mitochondrial genome known as kinetoplast DNA (kDNA) composed of maxicircles and minicircles. The kDNA structure and replication mechanism are divergent and essential for parasite survival. POLIB is one of three Family A DNA polymerases independently essential to maintain the kDNA network. However, the division of labor among the paralogs, particularly which might be a replicative, proofreading enzyme, remains enigmatic. De novo modeling of POLIB suggested a structure that is divergent from all other Family A polymerases, in which the thumb subdomain contains a 369 amino acid insertion with homology to DEDDh DnaQ family 3'-5' exonucleases. Here we demonstrate recombinant POLIB 3'-5' exonuclease prefers DNA vs RNA substrates and degrades single- and double-stranded DNA nonprocessively. Exonuclease activity prevails over polymerase activity on DNA substrates at pH 8.0, while DNA primer extension is favored at pH 6.0. Mutations that ablate POLIB polymerase activity slow the exonuclease rate suggesting crosstalk between the domains. We show that POLIB extends an RNA primer more efficiently than a DNA primer in the presence of dNTPs but does not incorporate rNTPs efficiently using either primer. Immunoprecipitation of Pol I-like paralogs from T. brucei corroborates the pH selectivity and RNA primer preferences of POLIB and revealed that the other paralogs efficiently extend a DNA primer. The enzymatic properties of POLIB suggest this paralog is not a replicative kDNA polymerase, and the noncanonical polymerase domain provides another example of exquisite diversity among DNA polymerases for specialized function.