Biblical principle:
Remarriage of a divorced woman is adultery; nothing could be clearer in Scripture.
"Whosoever marrieth her that is put away from her husband committeth adultery." - Lu 16

This is indeed the reason why the exception for putting away an adulterous woman is not an exception to "let not man put asunder"; if they were asunder, then remarriage would be no different from marriage. Rather, the covenant continues, remarriage is adultery - putting away, for a righteous man, is an alternative to making the woman a public example.

"Then Joseph her husband, being a just man, and not willing to make her a publick example, was minded to put her away privily." - Mt 1

Only death dissolves the covenant of marriage, not "as good as dead", or "dead to me", or whatever excuse an adulterer wishes to make.

"Know ye not, brethren, (for I speak to them that know the law,) how that the law hath dominion over a man as long as he liveth? For the woman which hath an husband is bound by the law to her husband so long as he liveth; but if the husband be dead, she is loosed from the law of her husband. So then if, while her husband liveth, she be married to another man, she shall be called an adulteress: but if her husband be dead, she is free from that law; so that she is no adulteress, though she be married to another man." - Ro 7

The divorced woman is bound by the law (this is a Torah community) so long as her husband lives. For the adultery of marrying a divorced woman there is one answer:

"Now the works of the flesh are manifest, which are these; Adultery, fornication, uncleanness, lasciviousness, idolatry, witchcraft, hatred, variance, emulations, wrath, strife, seditions, heresies, envyings, murders, drunkenness, revellings, and such like: of the which I tell you before, as I have also told you in time past, that they which do such things shall not inherit the kingdom of God." - Ga 5