Mitchell is credited with devising the novel enforcement mechanism in the Texas Heartbeat Act, also known as Senate Bill 8 (or SB 8), which outlaws abortion after cardiac activity is detected and avoids judicial review by prohibiting government officials from enforcing the statute and empowering private citizens to bring lawsuits against those who violate it.[4][5] On September 1, 2021, the Supreme Court of the United States refused to enjoin the enforcement of SB 8, marking the first time that a state had successfully imposed a pre-viability abortion ban since Roe v. Wade.[6]
Mitchell has argued five times before the Supreme Court of the United States and authored the principal merits brief in eight Supreme Court cases.[1] Mitchell has also written amicus curiae briefs in the Supreme Court. In Dobbs v. Jackson Women's Health Organization, Mitchell and a colleague urged the Supreme Court to overrule Roe v. Wade, arguing that overturning Roe should eventually lead to the reversal of other "lawless" court decisions such as those establishing a right to same-sex marriage (Obergefell v. Hodges), while distinguishing and defending the right to interracial marriage recognized in Loving v. Virginia.[13] [14]