The mind is a part of the inner man, the soul.
Paul is plainly showing that sin dwells in our flesh, that is to say our physical body.
Therefore
do not let sin reign in your mortal body, that you should obey it in its lusts. And
do not present your members as instruments of unrighteousness to sin, but present yourselves to God as being alive from the dead, and your members as instruments of righteousness to God.
Romans 6:12-13
Do you not know that
to whom you present yourselves slaves to obey, you are that one’s slaves whom you obey, whether of sin leading to death, or of obedience leading to righteousness? But God be thanked that though you were slaves of sin, yet you obeyed from the heart that form of doctrine to which you were delivered. And having been set free from sin, you became slaves of righteousness.
I speak in human terms because of the weakness of your flesh. For just as you presented your members as slaves of uncleanness, and of lawlessness leading to more lawlessness,
so now present your members as slaves of righteousness for holiness.
Romans 6:16-19
Paul is showing us that we have dominion over the sin in our physical body, because of the Spirit that dwells within us.
For I delight in the law of God according to the inward man. But I see another law in my members, warring against the law of my mind, and bringing me into captivity to the law of sin which is in my members. Romans 7:22-23
For what the law could not do in that it was weak through the flesh, God did by sending His own Son in the likeness of sinful flesh, on account of sin:
He condemned sin in the flesh, that the righteous requirement of the law might be fulfilled in us who do not walk according to the flesh but according to the Spirit. Romans 8:3-4
By the power of the Spirit within us, we ourselves are to put to death the sinful deeds of the flesh.
Therefore, brethren, we are debtors—
not to the flesh, to live according to the flesh. For if you live according to the flesh you will die; but if by the Spirit you put to death the deeds of the body, you will live. Romans 8:12-13
- but if by the Spirit you put to death the deeds of the body, you will live
JLB