According to N.T. Wright, Romans 12:2 “stands alongside [12:1] as the head of the whole section [12-15].” Paul’s point: those who are in Christ are to live in this world as if they were in the New World. Just as they were to offer themselves as a sacrifice, so they were to be spiritually renewed in the mind.

12:1 emphasized body (with mind); 12:2 emphasizes mind (with body).
I suggest not being conformed to this world will have, as at least one of its central themes in Paul’s sense of how the Romans should live, an emphasis on learning to avoid abuse of power and to avoid boundaries between Jews and Gentiles — both in perception and in relationships.
A Christian mind involves being renewed mentally through the Spirit; being able to discern God’s will — which means here rendering judgment in new situations (e.g., this is more than knowing that murder is wrong); and the discernment manifests in pursuit of what is good, acceptable, and perfect.