God cannot die because he is, and always has been, immortal. Immortal means that you cannot possibly die. 1 Timothy 6:16 (WEB) - "[
God] alone has immortality, dwelling in unapproachable light; whom no man has seen, nor can see: to whom be honor and eternal power. Amen."
Jesus is not God, he is God's only begotten Son, who was not immortal. God transformed him from a mighty mortal spirit being into a human being, and Jesus sacrificed his life on the cross and died. Three days later God resurrected Jesus to life again, this time giving him the divine, immortal, nature (just as He has promised for the Church).
1 Peter 3:18 (WEB):
Because Christ also suffered for sins once, the righteous for the unrighteous, that he might bring you to God; being put to death in the flesh, but made alive in the spirit;
2 Peter 1:4 (WEB):
by which he has granted to us his precious and exceedingly great promises; that through these you may become partakers of the divine nature, having escaped from the corruption that is in the world by lust.