Up until chapter 12, we have had doctrine. In these later chapters experience and practice are before us.
The people of Israel offered sacrifices of various types, such as animals or meal. A sacrifice in the New Testament could be service or a gift of money to gospel work, etc.
Because mercy was shown to us, it would be only our reasonable service to God to present our bodies a living sacrifice. It would not be a sacrifice unless it cost us something, labor, watching, money, serving the sick, etc.
We have been set free, and in the new power of the Spirit we present our bodies for God's use.
We now enjoy liberty and instead of being under law, an iron rule, we gladly comply to serve the Lord as led by the Holy Spirit. We cannot be conformed to this immense system, the world, built by Satan to make man comfortable without God.
Through the renewing of the mind we can now do the will of God in a world that has departed from Him. In Eden, Adam needed no way; all was planned for man and for his good. Since the fall, God has provided a way for faith to walk through the vast labyrinth of wickedness. Christ has shown the way when here in this world, walking to the glory of God.
We seek and delight in God's will after the inner man. To be subject, sacrificing self to the will of God, hinders our setting up self, so that the mind may be set on things above.
In the following verses are gifts and duties. Here is the only place in Romans that the body (the assembly) is mentioned and that to show services and the place for each to serve. The service of each one should be in unfeigned love. Giving should be with cheerfulness.