We have many trees in our backyard. There are some trees that are annoying. They are a haven for squirrels and other vermin. The trees we have in mind are growing wild and covering a shed we use for our sukkah. Is there any halachah that prevents us from cutting down a LIVE tree?

Shalom, Thank you for your question. There are certain laws that relate to cutting down trees. The Torah states “Thou shalt not destroy the trees” (Deuteronomy 20, 19) and this law applies everywhere, both inside Israel and abroad. However this law applies only to fruit bearing trees. If the trees you are referring to are not fruit trees then one may certainly remove them. Even if they are fruit trees, there are certain cases when they too may be cut down completely. In general, when the loss outweighs the gain of the fruit from the tree it is permitted to cut them down. See for example the Rambam (Melachim 6, 9) who writes that it is permitted to cut down a tree that got old and does not produce more than a small amount which is not worthwhile troubling for. The amount an olive tree should produce in order for it not to be cut down is a quarter of a Kav (approx. 0.65 lbs.) olives, and a palm tree which produces a Kav (approx. 2.6 lbs.) dates should not be cut down. If the tree causes damage then it may be cut down. If for example it's roots threaten the drainage or water pipes – or even if it blocks out the light to a window (and mere trimming of the tree will not help), it may be uprooted. Another example would be where the trees bring vermin that cause damage (although in that case, if the tree still gave a good amount of fruit one should first examine if there are not other ways to get rid of the vermin). Even when one is allowed to cut down fruit trees some opinions hold that there is a spiritual negativity to such an act (see Chida in Chaim Sha’al A, 23) and advice that one should avoid having a Jew cut the tree down, but rather employ a non Jew to do so, as they are not commanded with respect to this law at all. However from the letter of the law even a Jew may cut down a fruit tree in cases where the damage caused by the tree is substantial. Blessings.