DNA is normally coiled tightly, then coiled tightly gain (like twirling a rubber band gets twists, then another series of twists). To use a portion, it has to be unwound. To copy it, the whole thing has to be unwound from one end to the other. Doxorubicin interaclates (taking up the space amino acids normally would occupy) between Topoisomerase 2 and the DNA strand.
Growing cells have to do this to make more cells. And Cancer cells are among the fastest growing, so are among the hardest hit.
A simple analogy would be when the edge of you jacket's material get caught in the zipper and gets stuck.
With a broken zipper, the cancer cell is doomed.