"For even the Son of Man came not to be served but to serve, and to give his life as a ransom for many." - Mark 10:45
The word deacon (Gr. "diaconos") literally means servant. Sometimes, the word is used generically and refers to how every Christian is supposed to be serving and ministering like Jesus did. Sometimes, the word is used as a title and refers to the office of deacon in the church.
Used generically
Matt 20:26; 2 Cor 3:6; Eph 4:12; Rom 12:7; Matt 8:15; Mark 10:45
Used as a title
Philippians 1:1; 1 Tim 3:8, 12; possibly Rom 16:1
Acts 6 is where we find the first deacons in the Bible (or at the very least proto-deacons who set the stage for the official office of deacon). In this passage we see that deacons are servants of the church. They are appointed by the church as a whole in order to take the lead in problem solving and preserving the unity in the church. These men show exemplary character and are trusted to lead through service. It is no wonder that God says in 1 Timothy 3 that those who serve well as deacons gain a good standing for themselves - this is role of servant is an honorable position as our Savior demonstrated.
1 Timothy 3 gives us the qualifications for deacons. I won't go through every qualification here, but as you can see in this list of qualifications, the character of the deacon is the most important qualification. This list is not comprised of abilities or special skill sets learned through certain experiences. It is comprised solely of character qualifications, and that must not be understated (I'll be preaching on the topic of deacon qualifications on 10/3/21, so check the sermon on the website for more on this topic).
The qualification I want to look at briefly here is the "husband of one wife" qualification - literally "one woman man." Does this mean that a deacon cannot have ever been divorced, that a deacon must only have been divorced if it was under the parameters of the 'exception clauses' in the Bible, or does this only refer to the deacon's current fidelity to his wife regardless of previous marriages?
The relevant texts on marriage and divorce in the Bible are 1 Tim 3:12; Matt 5:32; 19:9; Mark 10:11-12; Luke 16:18; Rom 7:2-3; and 1 Cor 7:10-16. These texts point out two things. 1) Marriage is meant to be a life-long covenant union between a man and a woman. This has always and will always be God's plan. 2) Divorce is permitted in the cases of sexual immorality and abandonment (generally, abuse is included under the abandonment clause).
These "exceptions" to the no-divorce plan of God are in the Bible for a reason, and we should expect that when 1 Timothy talks about marriage qualifications for a deacon, it is probably not setting a higher standard than Jesus set. For that reason, it would seem that "one-man woman" doesn't refer to someone who's never been divorced.
The third option is that this passage is referring to the current marriage a person is in, not a previous one (regardless of whether the divorce was according to the 'exceptions' or not). The support for this position is not necessarily a specific text, but the overarching flow of the Bible. Jesus takes sinners and makes them holy, we see this play out time and again in the life of countless people throughout the Bible. So the question is asked, "Why isn't God able to take someone previously divorced and make them into a great husband now?" And the answer is that He is able to do that (almost like "The Scarlet Letter" in real life). This is what grace is all about. The question is whether or not this person with this past who has been changed by grace is qualified to be in this position of deacon. And there are differences between churches on this topic.
So these are the positions to consider as we think about what a "one-woman man" refers to. the church as a whole must decide on a position on this, especially in a culture like ours where divorce rates are so high.