We report calculations with first-principles density-functional theory and Landau-Devonshire theory that provide an atomic-scale mechanism for the composition-and pressure-induced relaxor ferroelectrics. A multiphase with coexisted cubic structures (MPCCS) is found to correspond to any of the composition- and pressure-induced relaxor ferroelectrics. On the other hand, a normal ferroelectric without relaxor behavior is structurally characterized by a single phase. Furthermore, the presence of the MPCCS in a composition-and pressure-induced relaxor increases the degrees of freedom of relaxors and no energy barriers are involved for the rotations of the polarization direction, leading to high electromechanical coefficients.