I can’t say it any better that R. C. Sproul:
 
”We believe that Jesus Christ was God incarnate. We also believe that Jesus Christ died on the cross. If we say that God died on the cross, and if by that we mean that the divine nature perished, we have stepped over the edge into serious heresy. We should shrink in horror from the idea that God actually died on the cross. The atonement was made by the human nature of Christ. Somehow people tend to think that this lessens the dignity or the value of the substitutionary act, as if we were somehow implicitly denying the deity of Christ. God forbid. It’s the God-man Who dies, but death is something that is experienced only by the human nature, because the divine nature isn’t capable of experiencing death.”
 
To see more go to: www.ligonier.org/blog/it-accurate-say-god-died-cross/
 
Let’s let Scripture explain:
 
1 Timothy 2:5–6 (ESV)
5 For there is one God, and there is one mediator between God and men, the man Christ Jesus, 6 who gave himself as a ransom for all, which is the testimony given at the proper time. It is the MAN Jesus who is the mediator between us sinners and a holy God.
 
Romans 5:19 (ESV)
19 For as by the one man’s disobedience the many were made sinners, so by the one man’s obedience the many will be made righteous. The one man, Adam, disobeyed God and brought sin into the world of men. It was the one MAN, Jesus, who lived in perfect obedience to the Father that paid for our sins by his death. Jesus the man died on the cross. A perfect man had to die for us. He did not die just as God’s son, but he also died
as the Son of Man.
 
Look at it this way: When God made you, he made you spirit, soul, and body. If you were to be hung on a cross to die, all of you would experience the agony of dying, but only your body would cease to exist and only until God someday gives you a new body. The spirit and soul of you would continue to be alive with the Father.
 
Jesus fully experienced the agony of the punishment for our sins, but only his human nature (body) ceased to exist and only then until he was raised in a new body. Jesus never ceased to be the third person of the Trinity, because God’s essence is three persons in one. If you take away 1/3 of the essence of God, God ceases to exist because God is eternally three persons in one essence. If God for one moment ceases to exist, everything ceases to exist. Acts 17:28 (ESV) “ ‘In him we live and move and have our being’…”