Apothnesko is the Greek verb rendered “die” in Hebrews 9:27. Its first use is in Matthew 8:32, in reference to a herd of pigs dying in the sea through drowning. Hence, apothnesko clearly can refer to biological death. However, apothnesko is also the verb the apostle Paul uses six times in his discussion of baptism in Romans 6:1-11. To understand the implications of Hebrews 9:27, we need to consider this passage.
What should we say, then? Should we go on sinning so that grace may increase? Of course not! How can we who died as far as sin is concerned go on living in it? Or, don't you know that all of us who were baptized into union with the Messiah Jesus were baptized into His death? Therefore, through baptism we were buried with Him into His death so that, just as the Messiah was raised from the dead by the Father's glory, we too may live an entirely new life. For if we have become united with Him in a death like His, we will certainly also be united with Him in a resurrection like His. We know that our old natures were crucified with Him so that our sin-laden bodies might be rendered powerless and we might no longer be slaves to sin. For the person who has died has been freed from sin.
Now if we have died with the Messiah, we believe that we will also live with Him, for we know that the Messiah, who was raised from the dead, will never die again; death no longer has mastery over him. For when He died, He died once and for all as far as sin is concerned. But now that He is alive, He lives for God. In the same way, you too must continuously consider yourselves dead as far as sin is concerned, but living for God through the Messiah Jesus. (International Standard Version)
Three times (verses 6:2, 10, 11), Paul uses the term “as far as sin is concerned,” signaling that he understands that, by using the verb apothnesko, he is not referring to biological death. He is referring to another species of death, one related to our separation from sin, not life. We could say he is delineating his use of apothnesko to refer to the specific sort of death he is discussing in the passage.
Romans 6:7, often mishandled by translators, nails down the understanding that Paul uses apothnesko metaphorically: “For the person who has died has been freed from sin.” This is the only passage in the Scriptures where some translators render dikaioo with the verb “free[d].” In virtually all other instances where dikaioo appears, translators render it as “justify” (or a similar word).
The Disciples' Literal New Testament properly renders Romans 6:7: “For the one having died has been declared-righteous from sin.” Plainly, Paul is not speaking of biological death, the result of which is not justification, not being declared righteous. The translators of this version recognize that Paul is not referring to biological death but to the death Christians experience at their baptism.
Their cue is verse 3, where Paul rhetorically asks, “Don't we know that all who are 'baptized into Christ Jesus [are] baptized into His death?'” In verse 7, as in all Romans 6, the apostle uses the verb apothnesko to refer to the first part of the act of baptism, the lowering of a person into the water, symbolizing death (that is, a burial).
Clearly, when Paul refers to Christians' being “crucified with” Christ (verse 6), he is neither talking about literal crucifixion nor literal death. Rather, he is talking about death as the first part of the act of baptism, the descent (burial) into the water. Consistently in Romans 6, Paul uses apothnesko (“to die”) in this sense.