When you came to Christ, you were “circumcised,” but not by a physical procedure. Christ performed a spiritual circumcision—the cutting away of your sinful nature.
As stated in this verse, circumcision means a cutting away, and in this reference it refers to a cutting away of the old sinful nature that used to reside on the inside. When you truly become born again, the real you on the inside died and a new spirit was birthed. The old has passed away and the new has come. The Lord removed the old sinful man on the inside so we can be transformed on the outside as well.
As Romans 12:1-2 tells us, we are to now present our bodies as a living sacrifice, holy and acceptable to God which is our reasonable response of worship unto Him. And we are to be transformed by the renewal of our mind, so that we can prove what is the good and acceptable will of God. This renewal of the mind is the key to seeing this new man change the way we live outwardly.
The key becomes what we renew our minds specifically to. We are to be renewed in our thinking to think in line with who we now are, what we now have, and what we can now do in Christ Jesus. Renewing of the mind means to change our thinking and then our actions to the new you. This is how we walk in this new nature, the very nature of God Himself that now resides in every born again believer.