Genuinely I just terminate any relationship and consider them to not exist. I don't get revenge, but there is no path to forgiveness for some things.
Discussion
But it entirely depends on what you are considering betrayal.
If someone knows you love banana splits, and then goes with friends for banana splits and doesn't invite you - that's not betrayal or not worthy of such response.
If you tell someone a secret in confidence and they tell someone very close to them and it gets out - that's not enough for me to cut them off. I know human nature too well to hold someone to such a standard.
"If you reveal your secrets to the wind,
you should not blame the wind for
revealing them to the trees."
Kahlil Gibran, The Wanderer