Strictly speaking, it is not possible to get a same-sex divorce in Texas because Texas law does not recognize same-sex marriages in any way. Even if a couple is married in another state and then moves to Texas, they could not get a divorce because they would not be legally married in Texas. This is because Texas law automatically declares any same-sex marriage to void.
While relationships similar to marriage, such as domestic partnerships, are not expressly recognized under Texas family law, they are still often upheld in court. One of the primary reasons a same-sex couple would wish to be granted a domestic partnership is in order to receive joint health benefits from an employer. The partnerships may also come into important for a couple with minor children that wish to have joint legal custody of the child.
Having a domestic partnership agreement is not the same as having a marriage. The same laws relating to marriage do not all apply to domestic partnerships. A domestic partnership agreement, however, can still be terminated if the couple decides to split up.
Like all couples, sometimes same-sex couples previously in a long-term relationship decide to end that relationship. Since the couple is not legally married and cannot file for divorce, they must address the issue of any cohabitation or domestic partnership agreements they may have made. If both individuals agree to annulment, then the process is usually simple. If one party does not agree, then the issue may need to be brought to court. Due to the fact that such situations in Texas are in a legal grey area, it is always best to have legal representation throughout the process.
Source: Texas Constitution and statutes, “SUBCHAPTER A. GROUNDS FOR DIVORCE AND DEFENSES“, October 05, 2014