Titus 3

Be Ready for Every Good Work

1 Remind them to be submissive to rulers and authorities, to be obedient, to be ready for every good work,

2 to speak evil of no one, to avoid quarreling, to be gentle, and to show perfect courtesy toward all people.

3 For we ourselves were once foolish, disobedient, led astray, slaves to various passions and pleasures, passing our days in malice and envy, hated by others and hating one another.

4 But when the goodness and loving kindness of God our Savior appeared,

5 he saved us, not because of works done by us in righteousness, but according to his own mercy, by the washing of regeneration and renewal of the Holy Spirit,

6 whom he poured out on us richly through Jesus Christ our Savior,

7 so that being justified by his grace we might become heirs according to the hope of eternal life.

8 The saying is trustworthy, and I want you to insist on these things, so that those who have believed in God may be careful to devote themselves to good works. These things are excellent and profitable for people.

9 But avoid foolish controversies, genealogies, dissensions, and quarrels about the law, for they are unprofitable and worthless.

10 As for a person who stirs up division, after warning him once and then twice, have nothing more to do with him,

KJV: A man that is an heretick after the first and second admonition reject;
Note KJV uses the word "heretick" rather than "divisive" person. Orginal Greek αἱρετικὸν hairetikon G141 hairetikos (hahee-ret-ee-kos'); Definition: causing division; Usage: disposed to form sects, sectarian, heretical, factious.

The heretic is one who forsakes the truth held by the Church, and chooses some doctrine of his own devising (αἵρεσις). The tendency of such departures from the doctrine of the Church to assume more and more of a deadly character, and to depart wider and wider from the truth, gave to the name of heretic a darker shade of condemnation in the mouth of Church writers as time advanced. But even in apostolic times some denied the resurrection (2Timothy 2:11-12); others denied the Lord that bought them (2Peter 2:1); and there were some who were of the synagogue of Satan (Revelation 2:9); so that already an heretical man, drawing away disciples after him, was a great blot in the Church.
Source: https://biblehub.com/titus/3-10.htm

We must be careful not to misinterpret the meaning of the word heretic based on the modern English meaning of the same word, but in this case, it seems the meaning of the original Greek word isn't that different from the modern English one. If after warning or rebuking the heretic twice he doesn't return to true doctrine, he was to be shunned or excommunicated. Heresy or false teaching was a serious problem in the early church, and it has been down through the ages, and it still is today. If anything, it's getting worse. False doctrine has crept into the church steadily, and seems to be increasing at an exponential rate. And it won't get better. The Bible warns us that false doctrine will get worse and worse with the coming of the Antichrist in the Great Tribulaton until finally Jesus himself returns to judge the living and the dead. Those Christians who say there are no heresies today, or that it is not our duty to root out false teaching are ignoring the warnings of Jesus and his apostles, and being disobedient to the Lord's commands. It is misguided to accept every and all beliefs whether they are true or not in the name of love and peace. The Lord and his apostles warned us against false doctrine in no uncertain terms. We would be fools, and disobdient ones, if we don't heed their warnings and commands.

11 knowing that such a person is warped and sinful; he is self-condemned.

A heretic is sinful, an evildoer. And you know what Jesus will say to evildoers on that day, don't you? "I never knew you. Away from me, you evildoers (Matt 7:23).". Heretics aren't Christians even if they claim to be. We must protect our vulnerable brethren from them. How? By pointing out their false doctrine and teaching true doctrine as it is written in Scripture.

Final Instructions and Greetings

12 When I send Artemas or Tychicus to you, do your best to come to me at Nicopolis, for I have decided to spend the winter there.

13 Do your best to speed Zenas the lawyer and Apollos on their way; see that they lack nothing.

14 And let our people learn to devote themselves to good works, so as to help cases of urgent need, and not be unfruitful.

15 All who are with me send greetings to you. Greet those who love us in the faith. Grace be with you all.