This verse is often used incorrectly to encourage non-violence and promote forgiveness. Non-violence and forgiveness are great attributes, but that is not what these two statements refer to. The verse is referencing generosity. If someone takes something from you (tangible items or other) they probably need it more than you do so why not help them out with meeting their needs. No one in history ever gave more to us than Jesus, who gave His life.
Lord, help me to understand that what mine is never mine and it is always Yours.