After creating Adam and Eve, God commanded them not to eat from the tree of the knowledge of good and evil, warning that if they ate from it then they would surely die.

Gen 2:16  And the LORD God commanded the man, saying, “Of every tree of the garden you may freely eat;
Gen 2:17  but of the tree of the knowledge of good and evil you shall not eat, for in the day that you eat of it you shall surely die.”

The fruit of this tree was not poisonous, as Adam and Eve went on to live for hundreds of years. So what killed them?  These verses do not state what the cause of death would be, only that they would die.  Adam and Eve went on to disobey God.

Gen 3:6  So when the woman saw that the tree was good for food, that it was pleasant to the eyes, and a tree desirable to make one wise, she took of its fruit and ate. She also gave to her husband with her, and he ate.

Several verses later we are told the consequences.

Gen 3:22  Then the LORD God said, “Behold, the man has become like one of Us, to know good and evil. And now, lest he put out his hand and take also of the tree of life, and eat, and live forever“—
Gen 3:23  therefore the LORD God sent him out of the garden of Eden to till the ground from which he was taken.
Gen 3:24  So He drove out the man; and He placed cherubim at the east of the garden of Eden, and a flaming sword which turned every way, to guard the way to the tree of life.

God banished Adam and Eve from the garden lest they ate of the tree of life and lived forever.  This means it was possible for them to live forever after eating from the tree of the knowledge of good and evil if they also ate from the tree of life.

Man is mortal.  He was not created with an immortal soul. (See “Do you have an immortal soul?”)  He needs to receive eternal life as a gift from God, as Romans 6:23 states.

Rom 6:23  For the wages of sin is death, but the gift of God is eternal life in Christ Jesus our Lord.

An essential part of attaining eternal life is receiving the Holy Spirit as Romans 8:11 explains.

Rom 8:11  But if the Spirit of Him who raised Jesus from the dead dwells in you, He who raised Christ from the dead will also give life to your mortal bodies through His Spirit who dwells in you.

Eating the fruit of the tree of life was symbolic of receiving the Holy Spirit.  Thus, when Adam and Eve where banished from the Garden of Eden, they were cut off from receiving the Holy Spirit and thus eternal life. They are not lost forever; they will have their chance of salvation in the second resurrection. (See “What are the Three Resurrections?“)

Conclusion

What killed Adam and Eve was being denied access to the tree of life.