Cell-cycle checkpoints and DNA repair processes protect organisms from potentially lethal mutational damage. Compared to other budding yeasts in the subphylum Saccharomycotina, we noticed that a lineage in the genus Hanseniaspora exhibited very high evolutionary rates, low Guanine-Cytosine (GC) content, small genome sizes, and lower gene numbers. To better understand Hanseniaspora evolution, we analyzed 25 genomes, including 11 newly sequenced, representing 18/21 known species in the genus. Our phylogenomic analyses identify two Hanseniaspora lineages, a faster-evolving lineage (FEL), which began diversifying approximately 87 million years ago (mya), and a slower-evolving lineage (SEL), which began diversifying approximately 54 mya. Remarkably, both lineages lost genes associated with the cell cycle and genome integrity, but these losses were greater in the FEL. E.g., all species lost the cell-cycle regulator WHIskey 5 (WHI5), and the FEL lost components of the spindle checkpoint pathway (e.g., Mitotic Arrest-Deficient 1 [MAD1], Mitotic Arrest-Deficient 2 [MAD2]) and DNA-damage-checkpoint pathway (e.g., Mitosis Entry Checkpoint 3 [MEC3], RADiation sensitive 9 [RAD9]). Similarly, both lineages lost genes involved in DNA repair pathways, including the DNA glycosylase gene 3-MethylAdenine DNA Glycosylase 1 (MAG1), which is part of the base-excision repair pathway, and the DNA photolyase gene PHotoreactivation Repair deficient 1 (PHR1), which is involved in pyrimidine dimer repair. Strikingly, the FEL lost 33 additional genes, including polymerases (i.e., POLymerase 4 [POL4] and POL32) and telomere-associated genes (e.g., Repressor/activator site binding protein-Interacting Factor 1 [RIF1], Replication Factor A 3 [RFA3], Cell Division Cycle 13 [CDC13], Pbp1p Binding Protein [PBP2]). Echoing these losses, molecular evolutionary analyses reveal that, compared to the SEL, the FEL stem lineage underwent a burst of accelerated evolution, which resulted in greater mutational loads, homopolymer instabilities, and higher fractions of mutations associated with the common endogenously damaged base, 8-oxoguanine. We conclude that Hanseniaspora is an ancient lineage that has diversified and thrived, despite lacking many otherwise highly conserved cell-cycle and genome integrity genes and pathways, and may represent a novel, to our knowledge, system for studying cellular life without them.