Casualties are removed by the player suffering them with the following restrictions. Casualties must be removed from the models in base contact with the enemy first, then from models that are fighting near the enemy (ie within 2"). Casualties are only carried over onto models more than 2" from an enemy where all other models have been slain. If an attack has been allocated against a specific enemy, then the wounds are only applied against that enemy model.
If a model has his opponent taken as a casualty before he has an opportunity to attack he may still attack another enemy model as if in base-to-base contact (remember the mêlée is a mobile swirling conflict not static as our models are, the attacker could have the opportunity to leap forward over the casualty to attack another opponent behind him). You may find it convenient to place the casualty on its side next to the model as a reminder that he fights in the combat with his full number of attacks.
As mentioned previously it's generally assumed that players will roll all attacks of the same Initiative value together to speed up close combats. However, if both players agree you can resolve attacks model by model. In this case simply remove casualties as they occur.
Errata — Chapter Approved: Main Rules Clarifications (v2.0): When removing casualties then the requirement that all models within 2" must be removed before those more than 2" away applies within each target unit as described above. For example, a unit of Chaos Space Marines with three men and a Champion in mêlée or within 2", and three others more than 2" away, suffers five casualties on the unit and none on the Champion. The three Marines in melee and two of those in support are killed even though the Champion remains within 2".
Errata — Chapter Approved: Main Rules Clarifications (v2.0): Models with multiple Wounds are removed when the unit they are in has taken enough wounds to eliminate one whole model regardless of whether the casualties were inflicted on different models. The owning player chooses which falls casualty. This is subject to the rule that characters may allocate attacks to a model in base-to-base contact.