Physical death is the separation of the soul from the body. Spiritual death, which is of greater significance, is the separation of the soul from God. In Genesis 2:17, God tells Adam that in the day he eats of the forbidden fruit he will “surely die.” Adam does fall, but his physical death does not occur immediately; God had another type of death in mind—spiritual death. This separation from God is exactly what we see in Genesis 3:8. When Adam and Eve heard the voice of the Lord, they “hid themselves from the presence of the LORD God.” The fellowship had been broken. They were spiritually dead.
A man without Christ is spiritually dead. Paul describes it as “being alienated from the life of God” in Ephesians 4:18. (To be separated from life is the same as being dead.) The natural man, like Adam hiding in the garden, is isolated from God. When we are born again, the spiritual death is reversed. Before salvation, we are dead (spiritually), but Jesus gives us life. “And you He made alive, who were dead in trespasses and sins,” (Ephesians 2:1). “When you were dead in your sins and in the uncircumcision of your sinful nature, God made you alive with Christ. He forgave us all our sins” (Colossians 2:13).
The book of Revelation speaks of a “second death,” which is a final (and eternal) separation from God. Only those who have never experienced new life in Christ will partake of the second death (Revelation 2:11; 20:6, 14; 21:8).
So, yes there are two deaths for those who remain in their natural, unredeemed state at physical death.