Casualties are removed from the rear rank, just like models killed by shooting attacks. Models that have stepped up to replace the fallen can fight, provided that their Initiative step has not passed.
With saving throws made or failed, you now need to remove the slain. Close combat casualties are removed in the same way as shooting ones. Although we can imagine casualties falling amongst the fighting rank, warriors in the ranks behind will step forward to fill any gaps that appear. Casualties will therefore be removed straight from a unit's rear rank. This means that if a unit is big enough, taking a handful of casualties will not reduce the number of Attacks the unit can make back.
It can happen that a model causes more casualties than it has enemies in base contact. The excess casualties are removed as normal from the unit as a whole, representing the attackers fighting over the fallen foes.
It is a good idea not to immediately remove models that are slain from the table, but instead temporarily place them next to their unit – you will need to know how many casualties have been caused when working out who won the combat.