Purity of heart, of course, suggests that all impurities have been purged. Paul describes the purging process in Romans 6:
What shall we say then? Are we to continue in sin that grace might increase? May it never be! How shall we who died to sin still live in it? Or do you not know that all of us who have been baptized into Christ Jesus have been baptized into His death? Therefore we have been buried with Him through baptism into death, in order that as Christ was raised from the dead through the glory of the Father, so we too might walk in newness of life. For if we have become united with Him in the likeness of His death, certainly we shall be also in the likeness of His resurrection, knowing this, that our old self was crucified with Him, that our body of sin might be done away with, that we should no longer be slaves to sin; for he who has died is freed from sin. (Romans 6:1-7)
In a Christian, the old self has been crucified. He is dead to sin, and slavery to sin is over.
Many people claim that this freedom from sin and death to sin are merely "positional," meaning that it is true only in God's perception, or a mere declaration by God, but not true in practical, day-to-day life.
This claim, of course, is false. First, there isn't a shred of textual evidence that this is any kind of "positional" truth that isn't also real practically. Second, the text demands that this is a practical freedom from sin. The first verse asks a question about continuing in sin, and Paul answers by saying that we can't continue in sin, because we died to it. If this death to sin were merely "positional," Paul's answer to the question about sinning wouldn't make sense. The reason he gives for not sinning is our death to sin, so this death must be a down-to-earth truth.
Thanks be to God for giving us real freedom from sin through Jesus Christ!