I have never seen or met the child I am Paying child support for in the state of Nevada. I went to court because the mother put child support on me, but she never showed up to court. I heard she has legal issues so that's probably why. Can I some how stop my child support payments if I take her to court myself and she doesn't show up again??

You petition the court to stop payments. If she doesn't show you ask the court to vacate the support order.

How did she get support on you in the first place?

You can ask, but I doubt it happens, have you confirmed paternity, do you know it is your child ?

I doubt they will stop child support, because she does not show up, since the order is in place. You may ask for a change in money, but that has to be proved.
You may ask for custody of the child, that way you get child and payments stop>
If she does not show, you may even be awarded custody

You say you went to court about CS, she didn't show, and you want to know if you can somehow get rid of the CS obligation. I'm confused, What was the nature of the hearing, and what did the judge do or say?