We derive an effective Lagrangian that facilitates the modeling of magnetization dynamics in a ferrimagnet with magnetization compensation point. The model is able to explain the earlier reported magnetization dynamics in the noncollinear magnetic phase triggered by a femtosecond laser pulse in GdFeCo amorphous alloy in the vicinity of spin-flop transition. Moreover, the described approach can be easily extended and applied to other cases of ultrafast magnetism in uniaxial f -d (rare-earth-transition metal) ferrimagnet near the magnetization compensation point in high magnetic fields. We assume that the primary effect of the femtosecond laser pulse is the ultrafast demagnetization of the ferrimagnet. We show that in the noncollinear magnetic phase, which can be prepared by applying external magnetic field above the spin-flop transition, such a demagnetization results in a torque acting on the magnetizations of both sublattices. It is shown that, similarly to the experiment, the amplitude and timescales of the dynamics strongly depend on temperature and applied magnetic field. In particular, in the vicinity of the spin-flop phase transition the amplitude dramatically increases while the dynamics exhibit a critical slowdown. We expect that the developed theoretical framework will boost further research of ultrafast magnetism of noncollinear spin systems.