"For the grace of God has appeared, bringing salvation for all people, training us to renounce ungodliness and worldly passions, and to live self-controlled, upright, and godly lives in the present age, waiting for our blessed hope, the appearing of the glory of our great God and Savior Jesus Christ, who gave himself for us to redeem us from all lawlessness and to purify for himself a people for his own possession who are zealous for good works." (Titus 2:11-14 ESV)
In my own words: Jesus died for sin that he might destroy sin. Or put another way: he died for my sins that he might deliver me from my sins. To redeem is to set free from bondage in order to bring us into a glorious, life-giving relationship with God.
Trust in Christ for salvation also means obedience to Christ for a new life. This too is included in "grace". Grace instructs us to renounce ungodliness and worldliness and lawlessness. There is a negative aspect to it -- but for a positive end: that we might have room for self-control, righteousness, godliness, hope, purity and zeal for goodness.
When the Lord removes something from my life it is so that he might replace it with something better.