A highly efficient, practical approach to high-energy multi-cycle terahertz (THz) generation based on spectrally cascaded optical parametric amplification (THz-COPA) is introduced. Feasible designs are presented that enable the THz wave, initially generated by difference frequency generation between a narrowband optical pump and optical seed (0.1–10% of pump energy), to self-start a cascaded (or repeated) energy downconversion of pump photons in a single pass through a single crystal. In cryogenically cooled, periodically poled lithium niobate, unprecedented energy conversion efficiencies >8% >8% achievable with existing pump laser technology are predicted using realistic simulations. The calculations account for cascading effects, absorption, dispersion, and laser-induced damage. Due to the simultaneous, coupled nonlinear evolution of multiple phase-matched three-wave mixing processes, THz-COPA exhibits physics distinctly different from conventional three-wave mixing parametric amplifiers. This, in turn, governs optimal phase-matching conditions, evolution of optical spectra, and limitations of the nonlinear process. Circumventing these limitations is shown to yield conversion efficiencies ≫10% ≫10% .