Relinquishing parental rights terminates only current support. If you owe back support you still have to pay it.
You can relinquish parental rights if there is a pending adoption (in most states). It's unlikely that a court would accept your relinquishment if the only purpose is to stop child support.
Assuming the other parent has a new spouse who wants to adopt, you should talk to the other parent and find out who the adoption attorney is that they'll be using. That attorney will likely have a form for you to use. Otherwise your local court should have a form. The form will be one in which you relinquish your parental rights and consent to adoption.
In many states the surrender of parental rights does not even modify your obligation to pay current child support until the child is adopted. It will not eliminate past support, unless there is some agreement, waiving the support and the child is being adopted. Most states will not accept your surrender of rights, unless there is an adoption proceeding pending or unless the child is in DSS custody and the Department is looking to have the child adopted. It is against public policy to take a parent away from the child unless there is someone available to replace the parent.