The spin-transfer-torque-driven (STT-driven) dynamics of a domain wall in an easy-axis rareearth transition-metal ferrimagnet is investigated theoretically and numerically in the vicinity of the angular momentum compensation point TA, where the net spin density vanishes. The particular focus is given on the unusual interaction of the antiferromagnetic dynamics of a ferrimagnetic domain wall and the adiabatic component of STT, which is absent in antiferromagnets but exists in the ferrimagnets due to the dominant coupling of conduction electrons to transition-metal spins. Specifically, we first show that the STT-induced domain-wall velocity changes its sign across TA due to the sign change of the net spin density, giving rise to a phenomenon unique to ferrimagnets that can be used to characterize TA electrically. It is also shown that the frequency of the STTinduced domain-wall precession exhibits its maximum at TA and it can approach the spin-wave gap at sufficiently high currents. Lastly, we report a numerical observation that, as the current density increases, the domain-wall velocity starts to deviate from the linear-response result, calling for a more comprehensive theory for the domain-wall dynamics in ferrimagnets driven by a strong current.