•Compressive behaviors of CTB depend on its component and confining pressures.•The solids content has a trivial effect on the friction angle of CTB.•The increased c/t ratio leads to a higher cohesion but a lower friction angle.•Lateral inertial confinement is more sensitive to the c/t ratio.•End-friction confinement is more sensitive to the solids content. A full understanding of the mechanical response of cemented tailings backfill (CTB) under various loading scenarios is beneficial for mining engineering applications. This study experimentally investigates the stress–strain response, failure pattern and criteria of CTB under triaxial compression loading with various confining pressures and components. Microstructural analyses are also conducted to reveal how the confining pressure influences the deformation behavior of CTB. Later, triaxial compression strength data are used to calibrate the constitutive parameters of the Holmquist-Johnson-Cook (HJC) model for CTB. Following the HJC model calibration, a split Hopkinson pressure bar (SHPB) model is established by using the commercial finite element software LS-DYNA to evaluate the effect of the lateral initial confinement and end-friction confinement on the dynamic compression strength of CTB with various components.