The underlying purpose in these instructions is not just humanitarian concern for other forms of life, but the preservation of a food source. A mother bird will lay more eggs and produce more young.
That it may go well with you, and that you may live long: this probably means more than a long life as such. It means the people will live for many generations in the Promised Land (see discussion at 6.2). Good News Translation gives a helpful model for this verse; so also does Contemporary English Version: “… Let her go free, and the LORD will bless you with a long and successful life.”
Quoted with permission from Bratcher, Robert G. and Hatton, Howard A. A Handbook on Deuteronomy. (UBS Helps for Translators). New York: UBS, 2000. For this and other handbooks for translators see here .
