Genome instability is a hallmark of cancer. The most common form of genome instability is chromosomal instability (CIN), a condition in which cells mis-segregate their chromosomes during cell division. CIN leads to aneuploidy, a state of karyotype imbalance, often found in tumors. Although the causal relationship between CIN and aneuploidy is well established, evidence is limited for a direct involvement of aneuploidy in promoting CIN. Here, we show that aneuploid cells experience DNA replication stress in their first S-phase and precipitate in a state of continuous CIN, eventually accumulating complex karyotypes. Mechanistically, we find that aneuploid cells fire dormant replication origins through a Dbf4-dependent kinase (DDK)-driven mechanism and complete replication of genomic loci through mitotic DNA synthesis (MiDAS). By following the fate of aneuploid cells, we also show that, when they divide, DNA damage can be distributed asymmetrically between daughter cells, and this may partially explain why some aneuploid cells are able to continue proliferating and others stop dividing. We further found that cycling aneuploid cells display lower karyotype complexity compared to arrested ones and increased expression of gene signatures associated to DNA repair. Interestingly, by stratifying aneuploid human cancer cells by their doubling times, we found the same DNA repair signatures to be upregulated in highly-proliferative cancer cells, which might enable them to keep proliferating despite the disadvantage conferred by aneuploidy-induced genome instability. In summary, our study reveals the origins of genome instability following induction of aneuploidy and indicates the aneuploid state of cancer cells as a point mutation-independent source of genome instability, providing an explanation for the high occurrence of aneuploidy in tumors.