The subject here is not the doing away with laws but the change in administration of existing laws. Remember that Jesus said not one jot or tittle will pass from the law (Matthew 5:18). In Hebrews 8:10, where the context is the Covenant, the New Covenant is shown to have laws, which will be written in our hearts.
Paul is making a comparison, showing the superiority of the ministry's responsibility under the New Covenant to the priesthood's responsibility under the Old. He compares ink with spirit, stone with flesh, letter with spirit (or intent), and death with life.
The "ministration of death" was Israel's civil administration for punishing violations of civil law. The laws were not done away, but the Old Covenant administration and enforcement of the law was set aside because the church does not have civil authority. It is that simple.
The church does not have civil authority over the state. However, the ministry has the opportunity to play a large part in the ministering of life to those God calls—through teaching and administering God's Word. Thus, the letter killed because the Old Covenant could not provide for life. Words—even of divine origin—cannot produce life. A vitalizing Spirit must be present to charge the words with transforming power.
Under the Old Covenant, God did not promise His Holy Spirit, forgiveness of sin, access into His presence, or eternal life. Jesus raised the civil law from its merely carnal application to the nation of Israel to its spiritual application to the church, which would be drawn from all of mankind, including, of course, the Gentiles.