When a server is giving poor service, I am not going to tip them.
What is make the service, "poor?"
Well she didn't even smile when I greeted her politely.
It is ok not to tip if you think service was poor.  Just make sure you don't overreact to a small infraction.
It's not you that has to tip her, she was just terrible.
Right, but not smiling is not a reason not to tip. You don't know what is going on with her. Now if the service was slow, food bad, rude server than you can not tip.