How can violence stop violence?

It doesn't.

A different Perspective:

Purveyors of violence understand only violence. While violence for violence is a circular path, a cycle, the most certain way to stop a violent action is to meet it with greater violence. This ensures that the fight or flight response is engaged, and the flight response is the most likely to be observed.

Survival is the greatest instinct of all life. If you challenge the belief that an attacker will not survive, he is not likely to attack. He is very likely to run away.

Additionally, if in the process of an attack you convince the attacker that he has made the most serious mistake of his life, one that is likely to cost him his life, he is likely to shift his intent from attacking you to trying to escape from you.

Consider the Cold War philosophy of MAD (Mutually Assured Destruction). In the wise, wise words of Sting, "...the Russians love their children too."

Never be the biggest bully on the block. Be the one who will beat the biggest bully to the ground when he comes to push you around.

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