Cells must replicate and segregate their DNA with precision. In eukaryotes, these processes are part of a regulated cell-cycle that begins at S-phase with the replication of DNA and ends after M-phase. Previous studies showed that these processes were present in the last eukaryotic common ancestor and the core parts of their molecular systems are conserved across eukaryotic diversity. However, some unicellular parasites, such as the metamonad Giardia intestinalis, have secondarily lost components of the DNA processing and segregation apparatuses. To clarify the evolutionary history of these systems in these unusual eukaryotes, we generated a high-quality draft genome assembly for the free-living metamonad Carpediemonas membranifera and carried out a comparative genomics analysis. We found that parasitic and free-living metamonads harbor a conspicuously incomplete set of canonical proteins for processing and segregating DNA. Unexpectedly, Carpediemonas species are further streamlined, completely lacking the origin recognition complex, Cdc6 and other replisome components, most structural kinetochore subunits including the Ndc80 complex, as well as several canonical cell-cycle checkpoint proteins. Carpediemonas is the first eukaryote known to have lost this large suite of conserved complexes, suggesting that it has a highly unusual cell cycle and that unlike any other known eukaryote, it must rely on a novel set of mechanisms to carry out these fundamental processes.