Texas Family Code, the governing body of law for such matters in Texas, considers parental duties and parental rights as two different things. You can give up your parental rights (posession, visitation, etc.) voluntarily or have them taken away from you. However, you cannot give up your parental duties, such as paying child support, even if you no longer have your parental rights.
You can, however, modify the child support amount if you are making less money than you did before, have a new family, or otherwise changed circumstances. However, the law behind such a change is complex. You need to discuss this with an qualified family law attorney in Texas and see if you are eligible for such a modification.