Whether one can remarry, then, is determined by whether or not the divorce itself was biblical.

The only other biblical grounds for divorce that I find in the Bible pertain to a divorce that an unbeliever seeks because he (or she) does not wish to live with a Christian spouse. I understand Paul to be instructing Christians not to divorce.

If they have already divorced, the must either remain single, or they can only re-marry each other.

I would remind you that this is a parallel passage to Matthew 19.

I understand that the reason why Jesus does not mention the exception in Mark's Gospel is that He is trying to emphasize "the rule" and not "the exception." That was the problem with the Pharisees.

It gave them the freedom to re-marry, without the guilt of committing adultery.

When I look at passages like Deuteronomy 24:1-4, it seems to me that divorce was granted so that the divorced party could remarry, without becoming guilty of adultery.He said that unless it was due to sexual immorality, the one who divorced his wife and married another would be committing adultery.Virtually everyone was shocked to hear what Jesus was saying.Some, He said, were born as eunuchs, while others were involuntarily made to be eunuchs.Some men even chose to become eunuchs for the sake of the kingdom.Realizing that Jesus gave no "easy out" from marriage, the disciples concluded that it might be better not to marry.