His human nature died; for He died not as God, but as man.
This comes to close to Nestorianism, in dividing the two natures of Christ. A more precise statement on Christology in regard to Christ's death can be found in the Angelic Doctor's Shorter Summa:
However, as we have shown above, on account of the union of the human nature with the Word of God in one person, whatever is said of the man Christ can rightly be predicated also of the Son of God. Consequently, since the personal union of the Son of God both with the soul and with the body of Christ remained in death, whatever is said of either of them could be predicated of the Son of God. Hence the creed asserts that the Son of God was buried (for the reason that the body united to Him lay in the tomb) and likewise that He descended into Hell (because His soul descended).
To say that God died could be misunderstood, yet it is correct to say that the God-Man died on the cross. The Son of God truly tasted death for us.