2 Corinthians 3:6
made us able [enabled, sufficient, competent, adequate] ministers [servants] -- Paul was called by Christ Himself to be a ministers of the new covenant. 2 Corinthians 1:1.
the new covenant -- The covenant that provides forgiveness of sins through the death of Christ ( Jeremiah 31:31-34; Ezekiel 11:19; Matthew 26:28; Hebrews 8:7-12).
the letter kills -- This is a reference to the law of Moses (compare Romans 2:27; Romans 7:6). The law does not justify people; it only identifies sin and condemns (see Romans 3:20; Romans 8:2). Instead, people are justified by faith (see Romans 3:28 and note).
the letter kills, but the Spirit gives life. -- The letter kills because it results in spiritual death. Man’s inability to truly keep the Mosaical Law sentenced him to an eternal death (without a sacrifice of atonement, see notes on Romans 7:9-11; cf. Romans 5:12; Galatians 3:10). Here "spirit" stands for the New Covenant under Christ, and only through Jesus Christ can one have eternal life, and it is through grace. Romans 1:16; 1 Corinthians 1:18.
“not of the letter but of the Spirit” There is a series of comparisons.
1. stone versus the heart, vv. 2 Corinthians 3:3
2. letter versus spirit, v. 2 Corinthians 3:6
3. old service versus spiritual service, v. 2 Corinthians 3:7
4. ministry of death versus life, 2 Corinthians 3:7, 2 Corinthians 3:6
5. the service connected with condemnation versus the service connected with right-standing, v. 2 Corinthians 3:9
6. what has passed away versus what is permanent, v. 2 Corinthians 3:11
7. the veil remains unlifted versus the veil is removed, v. 2 Corinthians 3:14
Paul is contrasting the old and new covenants, the contrast of the Law of Moses versus the Gospel of Christ, the "letter" versus the "heart" (cf. Romans 2:29; Romans 7:6), one depending on "legalism" versus "grace".
Not of the letter, but of the spirit -- Both in this and in the final clause of this verse, the RSV has perpetrated a gross error in capitalizing "Spirit" in order to make it mean "Holy Spirit" in both clauses, an error slavishly followed in Good News for Modern Man, Phillips New Testament, The New English Bible (1961), and others. While it is true, of course, that the blessings of the new covenant may be enjoyed only by those who have received the blessed Holy Spirit, there is no reference to that here. As Hughes said, "It is unlikely that a direct reference to the Spirit is intended." "The contrast in 2 Corinthians 3:6 is not between the outward and inward sense of scripture, but between the outward and inward power of the Jewish and Christian dispensations." As Tasker put it, "Paul is distinguishing the new covenant from the old by using the contrasted categories of spirit and letter, life and death." Farrar gave the meaning as "Not of the law, but of the gospel." Paul’s usage of this same expression in Romans 2:28 f speaks of a true Jew as one who is a Jew in heart, IN THE SPIRIT, NOT IN THE LETTER. There is no need to multiply evidence that Paul used the same expression here exactly as he used it there. - Coffman