The integrity of wellbores is essential for the safe and efficient operation of drilling activities. Cement plays a critical role in this process, serving as a primary barrier that isolates the casing from the surrounding formation. To ensure the proper application of cement in wells, a thorough understanding of its mechanical properties is essential. Latex-modified cement stone (LMCS) offers significant advantages due to its anti-channeling, anti-corrosion, and mechanical characteristics. This study examined the mechanical properties of LMCS through uniaxial and triaxial compression and Brazilian splitting tests. Under uniaxial compression, the elastic modulus, Poisson’s ratio, and compressive strength of LMCS were found to range from 4.08 to 8.29 GPa, 0.05 to 0.46, and 15.82 to 22.21 MPa, respectively. In triaxial compression tests with confining pressures of 2 MPa, 4 MPa, 6 MPa, 8 MPa, and 10 MPa, the elastic modulus ranged from 4.48 to 6.87 GPa, Poisson’s ratio from 0.05 to 0.16, and compressive strength from 27.38 to 39.58 MPa. The tensile strength of LMCS ranged from 2.34 to 3.72 MPa. Moreover, the compressive strength of LMCS increased with confining pressure, showing enhanced resistance to failure due to the confining effect. However, the rate of increase gradually diminished. Strength criteria for LMCS, including Mohr–Coulomb and Drucker–Prager parameters, were derived from the triaxial compression tests. These strength criteria parameters provide a useful reference for developing the constitutive model of LMCS and for simulating triaxial compression conditions. The findings of this research offer valuable insights that can guide the construction of oil and gas wells.