Mechanical properties such as Young's modulus, Poisson's ratio, and strength are important parameters for evaluating the cement sheath integrity. However, the current triaxial testing methods for the mechanical properties of intact-cylinder cement specimens ignore the “ring” shape of the wellbore cement sheath and its nonuniform 3D stress distribution, which may lead to deviations from the actual mechanical properties of the wellbore cement sheath that can affect the theoretical analysis results. In this study, we designed a hollow-cylinder cement specimen to address the aforementioned conditions and conducted uni, tri, and multiaxial compression tests to analyze the differences in the deformation, damage, and mechanical failure of the hollow- and intact-cylinder cement specimens. It was found that under the same confining pressure, the Young’s modulus of the hollow-cylinder cement specimen with hole pressure was approximately 1.2 times that of the intact-cylinder cement specimen; however, the difference in Poisson’s ratio was not significant. The uniformity of the radial and circumferential stress distributions in the hollow-cylinder cement specimens was the main factor affecting the volumetric strain curves and the damage threshold. Under tri and multiaxial compression conditions, the deviatoric stress of the hollow-cylinder cement specimens was higher than that of the intact-cylinder cement specimens. Compared with the Mohr-Coulomb criterion, the twin-shear unified strength theory can more accurately reflect the relationships between the radial, circumferential, and axial stresses and the strength of the hollow-cylinder cement specimens. Through a failure test of the cement sheath based on a self-developed wellbore simulation device, it was verified that the mechanical properties of the hollow-cylinder cement specimens can better reflect the failure law of the wellbore cement sheath compared with intact-cylinder cement specimens. The findings of this study can contribute to the understanding of the mechanical behavior of wellbore cement sheaths.