It's a metaphor, see: You put the killing thing right between your teeth, but you don't give it the power to do its killing.

This is a metaphor for how we can control our temper and our emotions. The quote is saying that when we find ourselves in a situation that makes us angry and we want to lash out, it is important to take control of our emotions and resist reacting in an aggressive way. The ‘killing thing’ is telling us not to give power to our negative emotions and to control our anger, rather than letting it control us.