Titus 3:10 - "Warn a divisive person once, and then warn them a second time. After that have nothing to do with them." 

What does divisive mean? Simply, it means those who create dissension or discord. Why is this such a destructive force? Simply, it DIVIDES people.  When a church is called to unity, this is the opposite behavior.  Unity is a big topic in the words that God left for Christians to follow.  It was a problem in some churches in the 1st century.  It is a problem in our church today.  Take some time to read the scriptures on unity.  Guard your hearts against a divisive person who destroys unity.  They are there.  They are wolves in sheep's clothing.  Matthew 7:15 - "Watch out for false prophets. They come to you in sheep's clothing, but inwardly they are ferocious wolves".  Wolves seek to separate and kill their prey.  Wolves seek to divide.  This is their nature. 

I Corinthians 1:10; Ephesians 4: 1-6; John 17:21; Philippians 2:3; Amos 3:3; Ephesians 4:3; II Corinthians 7:1; well, you get the idea...there is MUCH about unity!

What kinds of things do divisive people do to divide a group, and what are some reasons they may want to do this?  BIG QUESTIONS! There are probably as many answers to this question as their are people who divide, but if we look at the purest motives it would seem that selfishness is at the root of all of it.  James 3:14-16 - "But if you have bitter jealousy and selfish ambition in your hearts, do not boast and be false to the truth. This is not the wisdom that comes down from above, but is earthly, unspiritual, demonic. For where jealousy and selfish ambition exist, there will be disorder and every vile practice." They want what THEY want.  They seek to either obviously or, worse, subversively get their way.  This can be through gossip, Ephesians 4:29 - "Let no corrupting talk come out of your mouths, but only such as is good for building up, as fits the occasion, that it may give grace to those who hear." through false kindness to others with the intent to "win" their victim over to "their side", they may even try to blackmail others in a way to "force" their "WAY" on to I said the list can be endless. 

What do we do beyond having nothing to do with a divisive person.  One who seeks to live in dark places in their heart?  Ephesians 5:11 - "Take no part in the unfruitful works of darkness, but instead expose them." Read vs. 1-11...get a picture of what God wants of us as His children.  Exposing darkness in behaviors of others who seek to divide and conquer; exposing the divisive; is important in order for unity to be reestablished.  God was clear on these things. 
And, though this topic covered is in NO way all inclusive, one final thought for this is to remember our motivations when we work to eliminate divisive people, and darkness within our midst, is our true motive should be LOVE.  Love of the brethren, Love of our Lord, Love of His words, Love of ourselves in what kind of Godly person we strive to be.  However folks, LOVE is not weak, and it sometimes looks harsh.  Confused about this part?  Think of when you discipline your children...