How does setting your mind on the finished work of Christ and your identity in Christ cause you to live for Him?
"When you're free to be a child, you're not afraid to fail." - Heidi Baker
As Holy Spirit renews our mind and reveals to us our identity in Christ, our identity as the King's kid, that the finished work of the Christ tore away all that kept us from full fellowship with the Father, we're put in a place where every situation in our life is viewed from the perspective of who we are as seated in Heavenly places and having the Father on our side.
So this "causes us to live for Him" not in a way that we do things or we just act to impress Him, but we just know that God is already impressed with us because of what Jesus did, and we so overflow with the joy of God's grace and freedom and (most of all) love, that as we just live our lives become a fragrance pleasing unto the senses of the Lord.
This identity takes us from a place where we try to do things and puts us in a place of rest and joy and we just live and watch things happen for the Kingdom.