In the New Testament, there is only one acceptable reason for divorce and subsequent remarriage. That reason is the infidelity of one of the partners. Jesus' words are quite definite in Matthew 5:31,32 "Furthermore it has been said, ‘Whoever divorces his wife, let him give her a certificate of divorce.’ But I say to you that whoever divorces his wife for any reason except sexual immorality causes her to commit adultery; and whoever marries a woman who is divorced commits adultery." (NKJV)
My experience in the world and in counselling couples in these situations is that divorce almost always involves infidelity on the part of at least one of the partners. It is rare that couples divorce because of interpersonal issues in the marriage although financial stress is not an infrequent cause. What tends to happen is that issues in the marriage cause one or both partners to stray and that infidelity becomes the stress point upon which the marriage finally breaks down.
The ideal of marriage is the union of a man and woman for life. Again, the words of the Lord leave little or no "wiggle room" on this issue:
Mark 10:6-9 "But from the beginning of the creation God made them male and female. For this cause shall a man leave his father and mother, and cleave to his wife; And they twain shall be one flesh: so then they are no more twain, but one flesh. What therefore God hath joined together, let not man put asunder."
As modern society has strayed further and further from the way of life which God has ordained for us, sexual licentiousness and depravity become more and more the norm. Men are especially susceptible to the pressures of our society's neo-pagan morality and we see failed marriages at the rate of over 50% becoming the norm even among practicing "Christians." What should be the stand of a follower of Christ in such an environment? This subject raises huge issues around responsibility and fidelity - to God, to ourselves, our prospective mate, and to our children.
Here are the words of the prophet in Malachi 2:13-16 "And this is the second thing you do: You cover the altar of the LORD with tears, With weeping and crying; So He does not regard the offering anymore, Nor receive it with goodwill from your hands. Yet you say, "For what reason?" Because the LORD has been witness Between you and the wife of your youth, With whom you have dealt treacherously; Yet she is your companion And your wife by covenant. But did He not make them one, Having a remnant of the Spirit? And why one? He seeks godly offspring. Therefore take heed to your spirit, And let none deal treacherously with the wife of his youth. For the LORD God of Israel says that He hates divorce, For it covers one’s garment with violence, Says the LORD of hosts. Therefore take heed to your spirit, that you do not deal treacherously."
To enter into an unwarranted divorce is to put one's very salvation at stake.
What about a couple, having been divorced and remarried before they come to Christ? In Christ all things have become new. It is a fresh start. Sins are forgiven. Life begins refreshed and renewed. From that point on, divorce should not be an option.
What about those unhappy circumstances in which believers divorce and are married again to different partners and there is no adultery involved (I repeat, this is much rarer than you might think - adultery almost always rears its ugly head in such cases)? Then there is a need for prayerful and demonstrated repentance. Should that couple separate? I don't think there are hard and fast rules around that. However, such people must lose their ability to hold leadership/teaching positions within the congregation. These are the kinds of cases that give elders gray hair!
Here are links to information you will find useful:
Marriage in the Lord, Part 1 (please click on the title)
Marriage in the Lord, Part 2 (please click on the title)
I hope you have found this helpful.