Following prolonged mitotic spindle disruption by microtubule poisons, mammalian cells delay their entry into anaphase, then progressively slip out of mitosis and become tetraploid. Normal cells then stop cycling before S-phase onset, but the mechanisms underlying this arrest are still unclear. Here we show that a double block prevents endo-reduplication. First, cells that exit mitosis without a functional microtubule network are driven toward G0. Reconstitution of the network unmasks a second block that relies on DNA double-strand breaks occurring early in the G1 phase that follows the mitotic block. We propose that a stress signal elicited upon mitotic impairment triggers breakage, which couples the leaky spindle checkpoint to the stringent DNA damage response. Consistent with this finding, cells defective for the damage response continue cycling and acquire, within a single cell cycle, both chromosome rearrangements and abnormal chromosome numbers that remarkably mimic the complex genetic hallmark of tumorigenesis.