  We study the demagnetization dynamics of the fully compensated half-metallic
ferrimagnet Mn$_2$Ru$_x$Ga. While the two antiferromagnetically coupled
sublattices are both composed of manganese, they exhibit different temperature
dependencies due to their differing local environments. The sublattice
magnetization dynamics triggered by femtosecond laser pulses are studied to
reveal the roles played by the spin and intersublattice exchange. We find a
two-step demagnetization process, similar to the well-established case of
Gd(FeCo)$_3$, where the two Mn-sublattices have different demagnetization
rates. The behaviour is analysed using a four-temperature model, assigning
different temperatures to the two manganese spin baths. Even in this strongly
exchange-coupled system, the two spin reservoirs have considerably different
behaviour. The half-metallic nature and strong exchange coupling of
Mn$_2$Ru$_x$Ga lead to spin angular momentum conservation at much shorter time
scales than found for Gd(FeCo)$_3$ which suggests that low-power,
sub-picosecond switching of the net moment of Mn$_2$Ru$_x$Ga is possible.
