Put away... there is a Hebrew word for send away and a Greek word for send away. The context of Matthew 19refer back to Deuteronomy 24which has to do with sending away with a certificate in hand. The question the Pharisees asked was about putting/sending the wife away with a certificate. Putting away a wife without a certificate is not addressed in the Deuteronomy passage under discussion, nor was it in the question the Pharisees raised. Prior to the birth of Christ, the prince of the people, the most venerated scholar in the Sanhedrin, Hillel, and another highly regarded Shammai had disagreed on a number of issues. Both were Pharisees. Hillel was known for being very patient and a bit more liberal and laid back. Shammai was known for being impatient and strict. Hillel was more friendly toward Gentile conversion to Judaism, too. Hillel was stricter about having meet and dairy on the table at the same time than Shammai, but generally Hillel was more liberal.On marriage, Shammai believed that a woman had to have done something really bad, the uncleanness in Deuteronomy 24, for a Jew to legally divorce her. Hillel believed she just had to have displeased her husband. She could have burnt the food, for example. A wife, he and his followers believed, could be put away for any cause. So in Matthew 19, they discussed the 'any cause' divorce. Their go-to word for 'divorce' was their word for 'put away.' They would talk about sending away the wife, but the legal procedure required a certificate.There is a false teaching going around that ignores history and the actual wording of the passage that Jesus was just saying it was wrong to put away a wife without a certificate.I would imagine the interpretation of the exception clause would be that a man didn't have to give his wife paperwork if she'd fornicated under that interpretation, but I haven't seen someone promoting this carry this part to its logical conclusion.