We theoretically study the dynamics of ferrimagnetic domain walls in the presence of a Dzyaloshinskii-Moriya interaction. We find that an application of a dc magnetic field can induce terahertz spin-wave emission by driving ferrimagnetic domain walls, which is not possible for ferromagnetic or antiferromagnetic domain walls. The Dzyaloshinskii-Moriya interaction is shown to facilitate terahertz spin-wave emission in a wide range of the net angular momentum by increasing the Walker breakdown field. Moreover, we show that spin-orbit torque combined with the Dzyaloshinskii-Moriya interaction also drives fast ferrimagnetic domain wall motion by emitting terahertz spin waves in a wide range of the net angular momentum.