This entire passage points to the fact that we are free because Christ has made us free. We live through the power of the Holy Spirit working in and through our lives. We often recognize that the Bible teaches this, but we often communicate to God that we know better than Him and in essence communicate that we should be God.
We all have an internal problem of rebellion, sin, that no list of rules can help. It might help us look a little more moral and orderly for a time, but the reality is that we will still be walking aimlessly with no hope of salvation. But the good news is that Christ has made a way for us and our freedom in his life, death, and resurrection. And if you are attempting to mix the law and grace then you need to stop, repent, and turn to Jesus!
In closing, Paul shows us here that he is not one sided. It is not that he is against circumcision and for non-circumcision, but rather that he is all for Jesus as the way to salvation and nothing else. He basically says for the Gentiles not to boast in their un-circumcision and for the Jews not to boast in their circumcision because in the eyes of Christ both are irrelevant in terms of salvation.
So what might you be trying to mix with grace as means to your salvation? Or what might you be boasting in that is irrelevant in regards to salvation? Because whatever it is it is irrelevant and will never work, because as this passage shows us that salvation is in Christ Alone!