In Matthew 19, Jesus states that God ordained the institution of marriage, and He has decreed that in every marriage, the husband and wife are to become one for life. Divorce destroys the marriage and thus breaks asunder a union God Himself has established (Mark 10:9). "I hate divorce," says the Lord (Mal. 2:16).
Jesus' teaching on divorce is clear. He restricted divorce under most circumstances, and He forbade the remarriage of those who divorce on improper grounds, calling such remarriage adultery: "But I say to you that everyone who divorces his wife, except for the cause of unchastity, makes her commit adultery; and whoever marries a divorced woman commits adultery" (Matt. 5:32). The word "unchastity" in that verse is the Greek word porneia, "fornication"--which includes all kinds of gross sexual immorality.
The Old Testament contained a few provisions governing the remarriage of divorced people (Lev. 21:11, 14; Deut. 24:1-4). The rabbis had taken these laws and broadened them to permit divorce for virtually any reason. Under the rabbinical laws, if a wife displeased her husband in any way, he was entitled to divorce her. Jesus stated that this was never the purpose of Moses' Law. In fact, Jesus teaching on divorce was given specifically to refute the rabbinical loopholes. Furthermore, He so rigidly opposed divorce, that when He had completed His teaching, His disciples concluded that it would be better never to get married (Matt. 19:10)!
So God's utter hatred of divorce is very clear in Scripture.
Nonetheless, there are two extraordinary cases in which Scripture teaches that God does permit divorced people to remarry.
First, note that Jesus Himself included this exception clause: "Whosoever shall put away his wife, except it be for fornication, and shall marry another, committeth adultery" (Matt. 19:9, King James Version, emphasis added). He allows an exception in this one case, only "because of the hardness of your hearts" (Matt. 19:8). Clearly, Jesus is treating divorce as a last resort, only to be sought in the case of hard-hearted adultery.
The apostle Paul allows one more reason for divorce: if an unbelieving spouse abandons a believer, the believer is under no obligation in such a case (1 Cor. 7:14). This would free the abandoned spouse to remarry.
But we must emphasize that apart from those two specific, exceptional cases, divorce is not sanctioned in Scripture.