The Greek word for deacon (diakonos) means “serve” or “servant.” This same word is used several times in the Gospels to describe Jesus’ mission: he came not to be served (“deaconed”) but to serve (“deacon”) and give his life as a ransom for many (Matt 20.28, Mark 10.45, etc.). I love how Polycarp (d. ca. 160 AD) picks up on this, comparing the work of a deacon to Jesus’ work, the “Deacon of all.”
“Deacons (diakonoi)…[must be] servants (diakonoi) of God and Christ…acting in accordance with the truth of the Lord, who became a servant (diakonos) of all.”
Similarly, the “Constitutions of the Apostles” (written ca. 350 AD) noted that deacons serve the church just like Jesus served her. These “constitutions” said that deacons should not be ashamed
“To minister to those that are in want [need], as even our ‘Lord Jesus Christ came not to be ministered unto, but to minister and to give his life a ransom for many.’ If, therefore, the Lord of heaven and earth underwent all his sufferings for us, how then do you make a difficulty to minister to such as are in want [need], [you] who ought to imitate him who underwent servitude, and want [need], and stripes, and the cross for us?”
Even an old Reformed form for ordaining deacons reflects this.
“The office of deacon is based upon the interest and love of Christ in behalf of his own.”
In the church where I’m a pastor, we train deacons in order to help them fulfill their calling in Jesus’ church (cf. Acts 6). The bedrock of their training is this: Jesus humbling himself to be a servant, ultimately dying on the cross to serve and save sinful people. The gospel therefore is the foundation of the deaconate, the motivation for deaconal work, and the example for deacons to follow in their office. In other words, the office of deacon is a gospel-centered office.
(Above quote from Polycarp taken from The Apostolic Fathers – specifically Polycarp’s letter to the Philippians 5.2. The other quote was taken from volume 7 of the Ante-Nicene Fathers, page 432).