Okay, so just because Canaan is going to be annihilated does not mean that Israel was to destroy everything. God states that a special grouping is immune: fruit trees.
For full context, God forbids destroying fruit trees only during a siege. In those days, it was common for a nation that is besieging a town to use all available timber to make as many siege works as possible.
Instead, God wants these people to take a longer view. Instead of using up all the natural resources for a short-term benefit, think about your life after this city is taken. Will you benefit from this tree? Could its fruit supply you?
It seems like this was the way that Jews interpreted this passage. Instead of keeping it as a strict prohibition for just fruit trees, they expanded it to everything that was useful: clothing, food, water, and others.
This section also highlights God’s care for the land itself. Just like He wants Israel to let the land lay in rest every seventh year (Leviticus 25:1-7), so He also cares for the other things of nature. While they are there for our benefit, we can’t just destroy everything in our single-minded pursuit of a goal.
It’s impossible to talk about this verse without putting it into the context of the rest of Canaanite warfare. In other passages—and in this same chapter—God mandates the annihilation of people, whereas now, in Deuteronomy 20:19, God expressly saves fruit trees.
Does that seem hypocritical to you? If so, you’re in good company. A lot of people have disparaged God for valuing plants over human life, but the cause goes back to the original reason. A tree can’t influence Israel to sin. A tree can’t surrender. A tree can’t defy God.
Nations can, and did, for most of the time before Israel even showed up. Their practices were abhorrent; God delayed judgment for generations to give them time to repent (Genesis 15:12-16).
A tree is “not a man, that it can be besieged by you.” Just as He does elsewhere, the soul that sins will die. Fruit trees, quite literally by their nature, are exempt.