DNA topoisomerases are enzymes that modulate DNA topology. Among them, topoisomerase 3α is engaged in genomic maintenance acting in DNA replication termination, sister chromatid separation, and dissolution of recombination intermediates. To evaluate the role of this enzyme in Trypanosoma cruzi, the etiologic agent of Chagas disease, a topoisomerase 3α knockout parasite (TcTopo3α KO) was generated, and the parasite growth, as well as its response to several DNA damage agents, were evaluated. There was no growth alteration caused by the TcTopo3α knockout in epimastigote forms, but a higher dormancy rate was observed. TcTopo3α KO trypomastigote forms displayed reduced invasion rates in LLC-MK2 cells when compared with the wild-type lineage. Amastigote proliferation was also compromised in the TcTopo3α KO, and a higher number of dormant cells was observed. Additionally, TcTopo3α KO epimastigotes were not able to recover cell growth after gamma radiation exposure, suggesting the involvement of topoisomerase 3α in homologous recombination. These parasites were also sensitive to drugs that generate replication stress, such as cisplatin (Cis), hydroxyurea (HU), and methyl methanesulfonate (MMS). In response to HU and Cis treatments, TcTopo3α KO parasites showed a slower cell growth and was not able to efficiently repair the DNA damage induced by these genotoxic agents. The cell growth phenotype observed after MMS treatment was similar to that observed after gamma radiation, although there were fewer dormant cells after MMS exposure. TcTopo3α KO parasites showed a population with sub-G1 DNA content and strong γH2A signal 48 h after MMS treatment. So, it is possible that DNA-damaged cell proliferation due to the absence of TcTopo3α leads to cell death. Whole genome sequencing of MMS-treated parasites showed a significant reduction in the content of the multigene families DFG-1 and RHS, and also a possible erosion of the sub-telomeric region from chromosome 22, relative to non-treated knockout parasites. Southern blot experiments suggest telomere shortening, which could indicate genomic instability in TcTopo3α KO cells owing to MMS treatment. Thus, topoisomerase 3α is important for homologous recombination repair and replication stress in T. cruzi, even though all the pathways in which this enzyme participates during the replication stress response remains elusive.