Although his divine nature shared in the experience of the agony of death and separation from the Father, only his body was placed in the tomb (p. 33)
If he is saying that God or the divine nature of Christ died when Jesus died on the cross then that means the eternal Tri-une God experienced death and separation and disruption of perfect fellowship. In other words, in my mind the very nature of God is destroyed. I quickly did an internet search to confirm my suspicions. Here is what I found from RC Sproul:
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. In fact, two such heresies related to this problem arose in the early centuries of the church: theopassianism and patripassianism. The first of these, theopassianism, teaches that God Himself suffered death on the cross. Patripassianism indicates that the Father suffered vicariously through the suffering of His Son. Both of these heresies were roundly rejected by the church for the very reason that they categorically deny the very character and nature of God, including His immutability. There is no change in the substantive nature or character of God at any time.
You can see the whole article by Sproul here. The article is a short excerpt from his book, The Truth of the Cross, which is a free download until April 30.