Mat 5:31-32 ESV "It was also said, 'Whoever divorces his wife, let him give her a certificate of divorce.' (32) But I say to you that everyone who divorces his wife, except on the ground of sexual immorality, makes her commit adultery. And whoever marries a divorced woman commits adultery." (see also Mark 10:11-12)
Mat 19:3-11 ESV And Pharisees came up to him and tested him by asking, "Is it lawful to divorce one's wife for any cause?" (4) He answered, "Have you not read that he who created them from the beginning made them male and female, (5) and said, 'Therefore a man shall leave his father and his mother and hold fast to his wife, and they shall become one flesh'? (6) So they are no longer two but one flesh. What therefore God has joined together, let not man separate." (7) They said to him, "Why then did Moses command one to give a certificate of divorce and to send her away?" (8) He said to them, "Because of your hardness of heart Moses allowed you to divorce your wives, but from the beginning it was not so. (9) And I say to you: whoever divorces his wife, except for sexual immorality, and marries another, commits adultery." (10) The disciples said to him, "If such is the case of a man with his wife, it is better not to marry." (11) But he said to them, "Not everyone can receive this saying, but only those to whom it is given."
The following is concerning a marriage between believers, not a marriage between 2 unbelievers or 2 unbelievers when one becomes a Christian. Paul has guidelines for such circumstances in 1 Corinthians 7:10ff.
Its not that remarriage is necessarily an unforgivable sin... but divorce for illegitimate reasons, and remarriage after a divorce for illegitimate reasons, will or can cause 2 people to live together in a state of constant adultery. God looks at marriage as a covenant, one made before Him. Its not merely a contract that can be kept if one happens to feel like it, or broken with impunity. And if a person breaks their covenant vows before the Lord, say for instance that a man or woman divorces their spouse for reasons other than marital unfaithfulness, the God will not recognize either the cessation of the original marriage, or the remarriage, if such a remarriage occurs. If God does not recognize the marriage relationshiop in the case of remarriage, then of course 2 people living together and having sex are not only committing fornication, since they are not marriaed in God's eyes, but worse, adultery is being committed as the first marriage is still valid, in God's eyes.
This doesn't necessarily mean that salvation is itself not all of grace. It is. But a person who is truly a Christian will not commit adultery voiding the marriage covenant. (though Christians unfortunately do commit adultery they are to repent, stop sinning, be reconciled to their spouse if their spouse will have them, if they fail to take these steps then there is no reason to consider them a Christian as they are willfully and purposely living in a constant state of rebellion and sin.) If such a person does commit adultery, then leaves their spouse merely because they want an "upgrade" there is no reason to consider such a person a Christian in the first place, so, again, its not about grace being denied a person if they are coming to Christ for salvation.
Further, a person who is truly a Christian will not marry a person who was wrongly divorced in the first place, as this person is still actually married. That God does not recognize an illegitimate marriage does not mean that God is not a God of grace and mercy. He is. But He is also a God of law and wrath. The 2 concepts (grace and mercy/law and wrath) must always be held together, for if we think that God couldn't possibly be so "mean" as to not condone a marriage between 2 people who claim to love each other and not recognize their marriage, and further, consider it adultery, we have injected a modern view of what God must be like, and further, what love "must" be like. Love does not mean that there is no law, no commandments by which the Christian must live their life. The Law does not save, but the law is still valid unless it has been abolished in some way by the coming of Christ. In the case of wrongful divorce and wrongful remarriage, this is not the case, it is still a valid commandment (to not wrongly divorce your spouse and wrongly remarry another) every bit as much as "you shall not murder" or "you shall not steal".
Can a person be forgiven if they murder or steal? Well of course. But is a person really asking for forgiveness, coming to Christ acknowledging Jesus as both Savior AND Lord (this means submitting to Christ's moral commands and serving Him with one's whole life) if they continue, in an unbroken way, of stealing and murdering? Of course not, no one should consider such a person's profession of faith as vaild or meaningful. So too, if a person wrongly divorces their spouse, and they wrongly remarries, they are living in a state of constant unremitting sin, willfully so. Thus they are in the same situation as a person who continues sinning in an unbroken unrepentant way.
Is this a "hard word"? Yes, especially in today's society where people can exchange spouse about like they trade in cars. They think that all that matters is their "happiness", and if their spouse is "not meeting their needs" or they "just don't feel in love with their spouse anymore" then society says "why of course you should be happy... whatever you want... you should do it... be happy"... but that is not God's way.
Probably the most helpful discussion I have read on this situation is that of John Murray in his book entitled simply "Divorce". And I have read a great deal on the issue from many points of view as my wife left me me for unbiblical reasons, so I spent over a year in great personal turmoil about how this siutation should be handled, what my response ought to be, what it was exactly that my wife had done, etc. So I guess that I am just saying that while I am no expert, I also am not an ivory tower academic observer searching out this issue out of idle curiosity or even for the good reason of just knowing what the bible has to say on the subject of divorce.
see also
http://www.the-highway.com/divorce_Murray.html
GIRS Summary Studies in Reformed Theology: of Marriage and Divorce (part 2)
blessings,
ken