John Lightfoot on Matthew 1:19

[But Joseph, being a just man, &c.] There is no need to rack the word just, to fetch out thence the sense of gentleness or mercy, which many do; for, construing the clauses of the verse separately, the sense will appear clear and soft enough, Joseph, being a just man, could not, would not, endure an adulteress: but yet not willing to make her a public example, being a merciful man, and loving his wife, was minded to put her away privily.

[To make her a public example.] This doth not imply death, but rather public disgrace, to make her public. For it may, not without reason, be inquired, whether she would have been brought to capital punishment, if it had been true that she had conceived by adultery. For although there was a law promulged of punishing adultery with death, Leviticus 10:10, Deuteronomy 22:22, and, in this case, she that was espoused, would be dealt withal after the same manner as it was with her who was become a wife; yet so far was that law modified, that I say not weakened, by the law of giving a bill of divorce, Deuteronomy 24:1, &c., that the husband might not only pardon his adulterous wife, and not compel her to appear before the Sanhedrim, but scarcely could, if he would, put her to death. For why otherwise was the bill of divorce indulged?

Joseph, therefore, endeavours to do nothing here, but what he might, with the full consent both of the law and nation. The adulteress might be put away; she that was espoused could not be put away without a bill of divorce; concerning which thus the Jewish laws: "A woman is espoused three ways; by money, or by a writing, or by being lain with. And being thus espoused, though she were not yet married, nor conducted into the man's house, yet she is his wife. And if any shall lie with her beside him, he is to be punished with death by the Sanhedrim. And if he himself will put her away, he must have a bill of divorce."

[Put her away privily.] Let the Talmudic tract 'Gittin' be looked upon, where they are treating of the manner of delivering a bill of divorce to a wife to be put away: among other things, it might be given privately, if the husband so pleased, either into the woman's hand or bosom, two witnesses only present.