At the end of this big passage wherein Paul is preparing Titus to lead and teach the people (3.1-11), we now see the advice given when Titus comes across a person who stirs up division.
As for a person who stirs up division, after warning him once and then twice, have nothing more to do with him, knowing that such a person is warped and sinful; he is self-condemned.
We see that Titus is to have patience with those who seek to stir up division (…warning him once and then twice…), but eventually the course of action taken against those who are going their own way or insisting on their own way within the community of God’s people is to have nothing more to do with him. The true punishment is being self-condemned, having lived a life totally inconsistent with everything Paul has taught Titus to teach.
We don’t go out of our way to disrupt the false teaching ways of those who stir up division by leaving the Orthodox and well-beaten path, we simply leave them alone and have nothing more to do with him.
This can seem counter-logical to us as people of action; that person is making problems within the church family so I must do something, but, on the contrary, the stronger punishment (and the model employed by the Lord in Romans 1.24-25) is actually just to leave people alone. People cannot stir up division if they are ignored, left alone, or by themselves.
This might seem like a harsh word to effectively close the teaching portion of his letter on, but, Paul is charging Titus with the care of God’s people, a heavy responsibility. Titus is there to feed the sheep, not hunt the wolves.
For you and for me, we would do well to take this principle and apply it to our own lives; when we disagree, when someone has a proven record of stirring up division, when someone is obviously teaching falsely, we are not to go out of our way to attack them, simply guide what the Lord has given you to guide. Protect your people from error, yes, feed them what accords with sound doctrine, yes, but leave alone the rest.