In this passage, it's the relationship to the Law that is severed. From Law to Christ, not from flesh to Christ. Once ruled by Law, now we are ruled by Christ. Once we were in flesh, now we are in spirit.
Agreed, those who have, and are led by, the spirit have died to the law - and Paul keeps that same teaching about the law vs the spirit going, and explains our continuing choice to be led by the flesh, or by the spirit with the warning that if we choose to live after the flesh, we will die.
Rom 8:12 Therefore, brethren, we are debtors, not to the flesh, to live after the flesh.
Rom 8:13 For if ye live after the flesh, ye shall die: but if ye through the Spirit do mortify the deeds of the body, ye shall live.
Rom 8:14 For as many as are led by the Spirit of God, they are the sons of God.
Maranatha