Dr. Marsh Wilkinson Jr, in his comments on this verse, writes:

The first part of this verse may be understood to mean a number of things, all of them plausible and not necessarily exclusive: (1) I am convinced that nothing but the blood of Christ can save me, and thus I have given up on the law and its system; (2) I am so dead to the world with its affections and lusts that it is as though I have been crucified with Christ; (3) I am one with Christ, and my will is completely His. Paul stated that he was not literally dead, yet he was not the same person that he once was, either. He had taken on Christ completely so that he had totally died to his own will and made the will of God one with his. He was still in the flesh, and yet he was living by faith and obtaining victory over sin. How did he do it? By the power of Jesus Christ, who loved him and died for his sins.

From Lesson 5: "Flesh vs. Spirit", Galatians and Ephesians, Adult Teacher's Insights, July 5, 2015.