Types of Trees Under the Prohibition
All Food-Producing Trees
All food-producing trees are included in the prohibition of: לא תשחית את עצה – “You shall not destroy its trees”. This includes olive trees, grapevines, fig trees, apple trees, pear trees, etc. Even trees shorter than three tefachim whose fruits are Ha’adamah are included (Nishmas Adam, Hilchos Berachos, Klal 51, ois 7, Mishnah Berurah 203:3, and Birchas Hashem, siman 1, ois 6)
Similarly, one would get malkus for cutting down a tree whose fruits are shehakol due to their insignificance, e.g., crab apples. This is because it is still called a “food-producing tree” (Shu”t Avnei Tzedek, Yoreh Deah 45).
Tea Leaves, Herbs, Etc.
Only a tree whose fruits are used is included in the prohibition. Trees whose leaves are used for their flavors but not actually eaten, e.g., tea plants or the like (Shu”t Pnei Mavin 100), as well as trees that produce medicinal herbs are not subject to the prohibition since they are not considered food-producing trees (Shu”t Radvaz, Vol. 1, siman 44 and 499).
Trees Planted on a Roof or In a House
When it comes to orlah, if a tree was planted on a roof filled with dirt, in a pot [even without a hole at the bottom], or on a balcony under the open sky, e.g., in a dirt-filled trough attached to the ground, it is considered to be planted in the ground (Yoreh Deah 292:26). Accordingly, one would also be liable for destroying it (Birchas Hashem, 1:8)
As far as a tree in a house, if it was planted in a pot with a hole at the bottom or in a dirt-filled trough on the floor of the house, it would seem that it is forbidden to destroy it. However, the poskim are unsure whether the same is true if it is in a pot without a hole (Birchas Hashem, same as above).
Cutting a Branch
If severing a branch or multiple branches of a fruit tree may cause the whole tree to dry up, one obviously violates the prohibition of destroying a tree if he does so, and it is also a sakanah (Shu”t Be’er Chaim Mordechai, Vol. 2, siman 17, and Shu”t Yad Eliyohu, Yoreh Deah 46). However, what if it won’t cause the tree to dry up?
The poskim argue about cutting down a branch or multiple branches in a destructive way. Some say this also incurs malkus, as there is no difference between cutting down a whole tree or part of a tree (Shu”t Mahari Basan, siman 101, Be’er Sheva, Tamid 29b, and Shu”t Beis Yitzchok, Yoreh Deah 142). Others say it is prohibited due to the rule of חצי שיעור אסור מן התורה, even though there is no malkus (Shu”t Beis Yitzchok). Yet others say it is forbidden on a rabbinical level just like destroying other items (Shu”t Chesed L’Avraham, Tinyona, Yoreh Deah 35).
Others say the prohibition is only to cut down a whole tree, but it is mutar l’chatchila to cut off part of a tree (Mishneh Lemelech, Hilchos Issurei Mizba’ech 7:3, Shu”t Beis Yaakov 140, Shu”t Pnei Mavin, Yoreh Deah 99 and Aruch HaShulchan, Yoreh Deah 116:13). Some stipulate that this is only if new branches will grow in place of the ones that were cut off (Shu”t Yad Yitzchok, Vol. 2, siman 259).
Part of the Branch
Some hold that it is only prohibited to cut off an entire branch, but if one leaves over part of the branch by its base, there is no prohibition (Shu”t Teshuvos V’Hanhagos, 5:392)
For the Tree’s Benefit
Obviously, there is no prohibition or danger involved in cutting a young tree’s branches to enable it to grow more branches and widen its canopy, pruning a grapevine each year to help it grow, or similar actions. This does not destroy the tree; on the contrary, it improves the tree (Shu”t Chikrei Lev, Yoreh Deah, Tinyona 11).