The phrase "dead to sin" only occurs once in the Bible. Roman 6:11 says, "Even so consider yourselves to be dead to sin, but alive to God in Christ Jesus." As Christians, we are dead to sin through our union with Christ. In other words, We are to consider ourselves as being free from the bondage of sin. Jesus is the one who bore our sins in his body on the cross (1 Peter 2:24), and we died with him when he was crucified ( Romans 6:6:8). So, the phrase "dead to sin" means that the Christian who is trusted in the work of Christ on the cross is no longer a slave of sin and is freed from it.
Consider these verses.
- Rom. 6:2, “May it never be! How shall we who died to sin still live in it?”
- Rom. 6:10, “For the death that He died, He died to sin, once for all; but the life that He lives, He lives to God.”
- Rom. 6:11, “Even so consider yourselves to be dead to sin, but alive to God in Christ Jesus.”
- Rom. 7:4, “Therefore, my brethren, you also were made to die to the Law through the body of Christ, that you might be joined to another, to Him who was raised from the dead, that we might bear fruit for God.”
The last verse, Romans 7:4 is particularly interesting and relevant to answer the question. Because of our union with Christ and because we were "in him" (a phrase used regarding representation, see 1 Cor. 15:22 and Federal Headship), it is said that when Jesus died on the cross, we died with him. The Bible says that you are free from the law when you have died. Therefore, because we have died with Christ, we have died to the law. What is interesting is that the law reveals our sin (Romans 7:7). But, if the law no longer has power over us because we died to it with Christ, then we are said to be dead to sin.
Sin has no power over us to condemn us because the consequence of sin, which is death (Romans 6:23) and separation from God (Isaiah 59:2), was satisfied by Christ when he died on the cross (1 Cor. 15:1-4).
The context of Romans 6:11 is revealing:
"For if we have become united with Him in the likeness of His death, certainly we shall be also in the likeness of His resurrection, 6 knowing this, that our old self was crucified with Him, that our body of sin might be done away with, that we should no longer be slaves to sin; 7 for he who has died is freed from sin. 8 Now if we have died with Christ, we believe that we shall also live with Him, 9 knowing that Christ, having been raised from the dead, is never to die again; death no longer is master over Him. 10 For the death that He died, He died to sin, once for all; but the life that He lives, He lives to God. 11 Even so consider yourselves to be dead to sin, but alive to God in Christ Jesus," (Romans 6:5-11)
Paul tells us in verse six that our old self was crucified with Christ and that we are no longer slaves of sin. In verse 8 he says we have died with Christ. Therefore, when we get to verse 11 we too consider ourselves dead to sin, dead to the power it has over us, and we are alive to the power of God in us.
So, The phrase "dead to sin" means the Christian is no longer under the power of sin.