Doxorubicin and etoposide are both inhibitors of DNA topoisomerase II.
When chromosomes replicate as a cell divides, the helical nature of DNA results in the daughter molecules being tangled up (catenated). Topo II is an amazing enzyme; it binds to DNA, cuts a gap in both strands, and then passes another DNA molecule through the gap. Thus it untangles DNA.
If you inhibit Topo II, two things happen. Firstly, the inhibition usually takes place after the first DNA molecule has been cut. Thus inhibiting Topo II causes severe double stranded DNA damage, which is hard for the cancer cell to repair, and it dies. Secondly, the physical entanglement which remains stops the clean separation of the chromosomes during mitosis. Depending on the Topo II inhibitor in use, this can trigger a cell cycle checkpoint which stops the cell dividing Downes et al, 1994, or can cause the cell to rip the chromosomes to pieces as it tries to separate them anyway. I worked in the same lab as Downes et al, above, and have done this experiment with several Topo II inhibitors, including etoposide and doxorubicin. It's quite spectacular.