bal tashchis

כִּֽי־תָצ֣וּר אֶל־עִיר֩ יָמִ֨ים רַבִּ֜ים לְֽהִלָּחֵ֧ם עָלֶ֣יהָ לְתׇפְשָׂ֗הּ לֹֽא־תַשְׁחִ֤ית אֶת־עֵצָהּ֙ לִנְדֹּ֤חַ עָלָיו֙ גַּרְזֶ֔ן כִּ֚י מִמֶּ֣נּוּ תֹאכֵ֔ל וְאֹת֖וֹ לֹ֣א תִכְרֹ֑ת כִּ֤י הָֽאָדָם֙ עֵ֣ץ הַשָּׂדֶ֔ה לָבֹ֥א מִפָּנֶ֖יךָ בַּמָּצֽוֹר

Abarbanel says that this mitzvah is chizuk for battle.  "Ki mimenu tochal" -- you are going to conquer the city you lay siege to and will then be able to enjoy the fruit of its trees.  Why wreck what will be your future home?

Apropos of it being Elul, many meforshim read this mitzvah as teaching us something about how to fight our battle with the yetzer ha'ra.  Doing teshuvah should not be a scorched earth policy where everything from the past is thrown out.  Don't destroy the trees that can produce fruit, the valuable elements of your old self that can be utilized to produce good.

(It occurred to me that how fitting it is that this pasuk should appear in this week's parsha, the week in which the gaon R' Zalman Nechemya Goldberg, הגרז"ן, was niftar.)

The Rambam in Hil Melachim 6:8 formulates this issur as follows:

אין קוצצין אילני מאכל שחוץ למדינה ואין מונעין מהם אמת המים כדי שייבשו. שנאמר לא תשחית את עצה. וכל הקוצץ לוקה. ולא במצור בלבד אלא בכל מקום כל הקוצץ אילן מאכל דרך השחתה לוקה. אבל קוצצין אותו אם היה מזיק אילנות אחרים. או מפני שמזיק בשדה אחרים. או מפני שדמיו יקרים. לא אסרה תורה אלא דרך השחתה:

A few points:

1) It's not just cutting down a tree which is assur, but even destroying the tree through a grama, like not watering it, is assur.  Chazal derive this from the fact that the pasuk uses the lengthy formulation of  "lo tashchis... lindoach alav garzen"  instead of just saying "lo tidach alav garzen."

2) Contrast the Rambam's formulation here with what his writes in Sefer haMitzvos lav 57:

שהזהירנו מהשחית האילנות כשנצור על עיר כדי להצר לאנשיה ולהכאיב לבם.

Here the Rambam adds that not only is cutting down the tree unnecessarily assur, but even if cutting down the tree serves the purpose of causing pain to the enemy, it is still prohibited.

Ramban (Sefer haMitzvos, mitzvos aseh that the Rambam left out #6) disagrees on two points.  Firstly, he counts eating the fruit as a mitzvas aseh in addition to the lav of bal tashchis:

נצטוינו כשנצור על עיר לאכול מן האילנות שבגבולה כל ימי המצור ואם נכרות אותם לבטלה דרך השחתה נעבור על עשה מוסיף על הלאו

Secondly, he holds that cutting down trees to strike fear in the heart of the enemy is permitted:

 אבל בצאתנו מעל ארץ אויב נשחית ונחבל כל עץ טוב וכן בימי המצור להצר לאנשי העיר בהשחתת האילנות שלא יחיו מהם כל זה מותר, לא אסרה תורה אלא השחתה בחנם

Maybe this issue relates to a different machlokes.

The gemara (B"K 91) writes that you can chop a tree down if the gain is "me'ulah b'damim."  Rashi and the Raavad explain the gemara as dealing with a case where the wood of the tree is more valuable than the fruit, e.g. the wood can be used to make a valuable piece of furniture.  The Rosh, however, says an even bigger chiddush: if the cleared land would be more valuable than the tree itself, e.g. you want to develop real estate there, you can chop the tree down.

In the Rashi/Raavad example, the net benefit is a direct result of having the wood from the tree.  In the Rosh's example, the tree poses an opportunity cost -- it's not the wood itself which provides a direct benefit, but it's having the land which is what's valuable.  Achronim debate whether Rashi/Raavad and Rambam's omission of the Rosh's example implies that they disagree with his chiddush or not.

Here too, in Ramban's case the wood from the tree is not being used to fashion a weapon.  The benefit from having the tree removed is indirect -- the enemy is deprived of food, the enemy perceives the battle is turning against them, etc.  Is that enough justification to allow chopping down the tree?

Achronim discuss whether it is permissible to chop a tree down l'tzorech mitzvah, e.g. for schach on your sukkah.  In this case the benefit may come directly from the wood of the tree, but it is an intangible, spiritual benefit which is motivating the behavior rather than a physical need.  Again, the question may be how narrowly or not to define "me'ulah b'damim."