As a Latin rite Catholic my Church holds that Jesus died as both man and God on the cross. I have a bit of trouble getting my head around GOD dying. Perhaps I am not seeing death as it is interpreted with reference to God, as dying is really NOT ceasing to exist in the spiritual realm, only the physical. That said this is the origin of the "God Killers" charge made against the Jews during various periods in my Church's history. Yes the death and resurrection of Jesus the man, but did God "die" too, and was God "resurrected"? I hope this possibly silly question makes sense.
In any case what is the Orthodox teaching on the death of the God nature of Jesus Christ?
In the faiths issues board, Catholics are allowed to clarify when some one makes a mistake with regard to their understanding of Catholicism. In that spirit, I offer the following.
Before we can understand how God died on the cross, we need to understand the incarnation itself. Catholics believe that Jesus Christ is both fully God and fully man, and yet he is one person. This is not to be interpreted in some contradictory fashion but we understand it as mean that the one eternal and divine person, God the Son, existed from all eternity as God, in communion with the other two persons of the Blessed Trinity. At a particular point in history (around 0 A.d.), God the Son assumed a complete human nature along side his Divine nature. That is how there is one person, God the Son/Jesus, with two natures.
Now because Jesus is God, everything that he ever did was done by by God (specifically God the Son). This would include his conception, birth, death, resurrection, ascension, etc. So it is quite proper to say that God died on the cross for our sins.
This can be a stumbling block for many, because they will ask the question, "How can God die?" Well, let 's first understand what death is. It is nothing more than the separation of the soul from the Body. It is true that this can only be done by some one with a human nature, because one must have both a soul and a body for this separation to occur. It is also true, that death does not the mean that one ceases to exist. Again, it is just the separation of the soul from body. This is quite possible for the God-man, Jesus Christ, because in his human nature, his soul was able to be separated from his body. Again, this does mean that he ceased to exist for a time, only that is body and soul were not united for the period in which he was dead. In his Divine Nature, he was still ruling the universe as the Almighty and Living
God, while in his human nature he was experiencing the separation of the soul from the body that is death.
Some might argue then that because the death did not come about through his Divine nature, then it is not proper to say that God died. But, we have to remember that Jesus Christ is one person, not two, and we don't say that a nature dies. We say that a person dies. While Christ's divine nature did not die, the person, Jesus Christ, who is God, did die, and so we say that God died for our sins.