First, let us define what "sin" is. It is an old English word in archery that means "missed the mark". If you did not hit the bullseye, you were called a "sinner". Now there are many sins (little s and plural) but there is only one Sin (capitol S and singular). Sin is a positional state that seperates you from God. When Christ died, He saved us from Sin. That is, the postitional state of being "in Sin" has been eliminated. Now do we continue to commit sins? Yes. It is hard to walk in this world and not get your feet dirty. 1 John 1:8 states,
"If we say that we have no sin, we deceive ourselves, and the truth is not in us."
However, now, because of Jesus, we can have a daily cleansing...
"If we confess our sins, He is faithful and just to forgive us our sins and to cleanse us from all unrighteousness."
We are now clean.
A good way to look at this is you deciding to adopt an orphan. You do the legal stuff and the child is no longer an orpan but your son or daughter. This is what Jesus did on the cross. Allowed us to become adopted into the family of God.
Romans 8:15 For you did not receive the spirit of bondage again to fear, but you received the Spirit of adoption by whom we cry out, “Abba, Father.”
Now, does your new child play in the mud and get dirty? Yes. That is what hoses and bath tubs are for. Is he/she still your child? Yes. Do they do things wrong and need discipline? Of course! Are they still your child? Yes.