In Matthew 19:9 and Mark 10:11-12 replace the word divorce with “separated” or “separates from” (as in still married) for the correct meaning from the Greek text.
Mark 10:11-12 “He said to them, “Whoever separates from his wife, and marries another, commits adultery against her. If a woman herself separates from her husband, and marries another, she commits adultery.”
Matthew 19:9 “I tell you that whoever separates from his wife, except for sexual immorality, and marries another, commits adultery; and he who marries her when she is [only] separated commits adultery.”
The phrase “against her” is key. It is not the act of marrying another, but the fact that the man separated and abandoned the wife. This would require that she marry another to survive thus forcing her into the situation of adultery. The husband who did this became guilty because he caused it to happen. This is the same as what happened in Malachi 2:14-16. There was no bill of divorcement.