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.