I'm going to cut an old friend I have issues with out of my life.
Is there a valid reason to cut them out?
I think it's the right thing to do.
It's obviously completely your decision about who you stay friends with, but cutting someone out of your life is a big step. They will feel shunned and hurt. So, maybe you should have a conversation with them first to see if you can smooth things over instead.
They deserve it.
It is still wrong to abandon your friends. I think you should talk with them and tell them how you feel about what happened. They might want to make things better with you.