http://www.gotquestions.org/did-God-die.html
Question: "Did God die? If Jesus was God, and Jesus died
on the cross, does that mean God died?"
Answer: Did God die when Jesus died on the cross? The
answer depends on how we understand the meaning of the word "die."
To die does not mean an end of existence. Death is separation.
Death is when the soul-spirit separates from the physical body. So,
in that sense, yes, God died, because Jesus was God in human form,
and Jesus' soul-spirit separated from His body. However, if by
“die” we mean a cessation of existence, then no, God did not die.
For God to die would mean that He ceased to exist, and neither the
Father, nor the Son, nor the Holy Spirit will ever cease to exist.
The essence of Jesus, the second Person of the Trinity, left the
body He temporarily inhabited on Earth, but His essence did not
die, nor could it.
Jesus is truly God and truly man. His physical body did die because
it was entirely human. Just as our physical bodies die, so did His.
But in the same way that Jesus died physically, but remained alive
spiritually, so our physical bodies will experience death, but our
soul and spirit will remain because they are eternal. The same is
true with regard to Jesus Christ. His physical body died, but His
inner being is eternal and could not die.
The question for all people to ask is “what will happen to my
soul/spirit when it leaves my physical body?” This is the most
crucial question in life. As we saw with Jesus, our spirits will
leave our bodies and travel on to somewhere else. Jesus returned to
heaven to be with the Father. We will either follow Him there to
spend eternity in heaven with Him, or we will go to hell to spend
eternity in “outer darkness” where there will be “weeping and
gnashing of teeth” (Matthew
8:12). There is no other option. Jesus’ physical
death on the cross paid the way for all who would ever believe in
Him so that we can know for sure where our spirits will reside for
eternity. His physical death provided to us spiritual life, both
here and in heaven. “And if the Spirit of him who raised Jesus from
the dead is living in you, he who raised Christ from the dead will
also give life to your mortal bodies through his Spirit, who lives
in you” (Romans
8:11).