# a covenant not of the letter

The phrase alludes to the Old Testament law. Alternate translation: "a covenant not based on commands that men have written" 

# but of the Spirit

"but a covenant of the Spirit" or "but a covenant based on what the Spirit does" 

# the letter kills

Paul speaks of the Old Testament law as a person who kills. Following that law leads to spiritual death. Alternate translation: "the written law leads to death"