This phrase is a particular bit of idiocy that never seems to die. And it is especially sickening given that it actually works against itself when invoked a deterrent.
If one is urged not to "react violently" for a violence already suffered, and obliges, the very phrase becomes untrue. Violence has stopped, and the original violence has not "begotten more violence." What then, does the peacenik say to discourage the original perpetrator from behaving violently again? That "violence will only beget more violence?" No, that's been stopped. There is no longer that deterrent. So the violence can now continue, undeterred by the squandered truth of the original observation.
Violence must always beget more violence. Otherwise it has no cost. And methods with no cost are used in great frequency, and never reserved for last resort.
Gandhi actually believed that Britain should have surrendered to Germany during WWII, and that Jews should adopt "active nonviolence" that "would melt the stony hearts" of Nazis stuffing them into ovens. That about says it all.