I assume by "intrinsic nature" you actually mean "divine nature". God is immortal in His divine nature. But because the Second Person of the Trinity has a human nature, and human nature is mortal, therefore God is mortal in His human nature.
Christ is eternal in His divine nature, temporal in His human nature.
Christ is indivisible in His divine nature, visible and composite in His human nature.
Christ is immutable in His divine nature, mutable in His human nature.
If God died then all of God died since God is one substance, indivisible.
That claim simply denies the incarnation, that whoever died on that cross was not God. The Second Person of the Trinity died that day on Calvary 2000 years ago. He died through His human nature, so that, although the Second Person of the Trinity did not cease to exist. In fact, He continued to uphold all things by the word of His power, just as He had done in from the beginning of creation, in Mary's womb and throughout His human life. But He truly died, because He was truly man, and when He breathed His last upon the cross, His human soul was separated from His body, so that He truly died, and remained dead until He rose from the dead on the third day.
-A8
Christ is indivisible in His divine nature, visible and composite in His human nature.
Christ is immutable in His divine nature, mutable in His human nature.
See? See? When I say this stuff I'M the Nestorian/Arian heretic. /whining ... LOL! :)