The "reed" (Matthew 12:20) is probably speaking of the reeds that grew in the marshy areas in the land of Palestine. These were very fragile and could be easily bruised or broken. The term "smoking flax" refers to a linen wick which was made from flax and burned brightly when floating on oil in an open lamp. When the oil was gone, the flax would just smoke until the oil was replenished.
The meaning of these illustrations is that Jesus is ministering in mercy to those who have been bruised or broken (Luke 4:18), and to those who have lost their oil (spirit). He has come to fill them anew (Matthew 5:3; Acts 1:5; 2:4).
The Jews were used to the judgment of the law but Jesus came to minister grace and truth (John 1:17), even to the Gentiles (Matthew 12:18, 21).
God's mercy to the believer is revealed by His act of taking away the misery of sin's consequences through the New Covenant of our Savior, the Lord Jesus Christ. Salvation is given to us because of God's mercy. It's not something we've deserved or earned.
As Paul said, "Not by works of righteousness which we have done, but according to HIS MERCY He saved us" (Titus 3:5). God is for us, not against us. We are to cast all of our cares upon Him, because His mercy endureth forever!