Clay-sulfate rock, due to its significant expansiveness, poses a major challenge to tunnel engineering design. Understanding its swelling potential, which includes both swelling strain and swelling pressure, is a key prerequisite for ensuring safe and stable tunnel design. Water significantly influences the swelling potential and constitutive model of clay-sulfate rock. Four types of swelling tests (FST, SPT, WSPT, and CLST) were carried out on clay-sulfate rock. The results show that with initial water contents of 0%, 3%, 6%, and 9%, the clay-sulfate rock exhibited average maximum swelling strains of 2.387%, 1.494%, 1.031%, and 0.739%, and average maximum swelling pressures of 1.843 MPa, 1.431 MPa, 0.992 MPa, and 0.752 MPa, respectively. Two SEXM (single exponential models) were proposed to quantitatively evaluate swelling strain and swelling pressure under varying water contents. At water pressures of 300 kPa and 600 kPa, the maximum swelling pressures of clay-sulfate rock with initial water contents of 0%, 3%, 6%, and 9% were 1.621, 1.368, 0.917, 0.569 MPa, and 1.124, 0.824, 0.467, 0.425 MPa, respectively. A three-dimensional double exponential model accurately describes the relationship between maximum swelling pressure, water content, and water pressure. A novel three-dimensional swelling stress–strain relationship for clay-sulfate rock, which for the first time incorporates water content effects, was also proposed and validated by the experimental results of other scholars.