Some do, I think that is a mistake.
Can God separate Himself from Himself?
The obvious answer is no.
When Christ died on the Cross, He said it was finished. This negates a possibility that the teaching "He was separated from God and underwent the Second Death."
Christ states...
John 16:32
King James Version (KJV)
32 Behold, the hour cometh, yea, is now come, that ye shall be scattered, every man to his own, and shall leave me alone: and yet I am not alone, because the Father is with me.
This is without controversy a context in which the Cross is in view.
No. I believe Jesus referred to when every one will be scattered. There is a different view on that cross when this was written.
Matthew 27:45 Now from the sixth hour there was darkness over all the land unto the ninth hour. 46 And about the ninth hour Jesus cried with a loud voice, saying, Eli, Eli, lama sabachthani? that is to say, My God, my God, why hast thou forsaken me?
Mark & Luke both testify also to this event when Jesus took our sins upon Himself that it was "reflected" in nature as the light from the sun, the light from the full moon, and the light from the stars all blinked out as an unexplainable darkness enveloped the world. The light of creation took our sins upon Himself.
2 Corinthians 5:20 Now then we are ambassadors for Christ, as though God did beseech you by us: we pray you in Christ's stead, be ye reconciled to God.
21 For he hath made him to be sin for us, who knew no sin; that we might be made the righteousness of God in him.
Thallus, a secular historian, recorded the darkness at His crucifixion as an eclipse, but Julius Africanus corrected him as saying it was unlikely because there was a full moon at that time. Therefore for that darkness to exist, where was the light from the full moon? Therefore the light from the stars were also affected for such a darkness to exists.
http://www.biblehistory.net/newsletter/crucifixion_darkness.htm
So the Son of God did experience a separation from God the Father.
What you are saying, if you say you separate the Son of God from the Father and Holy Ghost is that Christ was at that time no longer God. Just a man.
The Son of God was also the Son of Man, and the Son of Man had died, but Christ had the power to be alive again.
John 10:17 Therefore doth my Father love me, because I lay down my life, that I might take it again. 18 No man taketh it from me, but I lay it down of myself. I have power to lay it down, and I have power to take it again. This commandment have I received of my Father.
Scripture does not teach that.
Philippians 2:5 Let this mind be in you, which was also in Christ Jesus: 6 Who, being in the form of God, thought it not robbery to be equal with God: 7 But made himself of no reputation, and took upon him the form of a servant, and was made in the likeness of men: 8 And being found in fashion as a man, he humbled himself, and became obedient unto death, even the death of the cross.
This is His glory.
Philippians 2:9 Wherefore God also hath highly exalted him, and given him a name which is above every name: 10 That at the name of Jesus every knee should bow, of things in heaven, and things in earth, and things under the earth; 11 And that every tongue should confess that Jesus Christ is Lord, to the glory of God the Father.
Christ was and always remained God, though He veiled His glory in human flesh.
Can God die? The Son of God/Son of Man did. God the Father cannot, and neither can the Holy Spirit.
This is why I reject the statement of the Creed that states "We believe Christ to be the eternally begotten Son."
That is in error. Christ is not eternally begotten, the Incarnation was prophesied about and occurred at a particular time in the history of men. Now if that statement is taught as a reference to the foreknowledge of God, that is okay, but, we have to recognize that Christ came into being the day He was placed in Mary's womb.
Some will misunderstand what I am saying but it is just a Biblical Fact that Jesus Christ has a point in time when He came into being.
Actually, since it is written that no man has seen God the Father, but Jesus has, John 1:18 & John 6:46 , then Who was the God that men had seen in the O.T. by Abraham ( Genesis 18:1 ), Isaac ( Exodus 6:3 ), ( Genesis 32:24-30 ) Jacob & others ( Exodus 4:5 )? That was the Son of God.
Now the Son of God, that is Who is Eternally God. He is God, always has been, always will be.
Even on the Cross.
Yep. When He took our sins upon Himself, our Creator, the Light of the world, it did show in creation of what our Creator did for us as Witnessed by the Father & the Holy Spirit.