In Settlers 2 (PC), is it possible to get food back from an exhausted mine or otherwise prevent food waste?

The best way to deal with this is to destroy the mine as soon as it is exhausted. You'll lose any food inside it but food on its way will be sent to other mines or returned to storehouses.

You'll lose a small amount of food but it's not a big problem. Meat and bread are unlimited and 2 per mine is a tiny percentage of late-game food production.

The short and simple answer is no: it is not possible to retrieve food that has been placed in a mine.

Another way to reduce waste that I learned through playing is to not produce all 3 kinds of food. I personally found pig farming unnecessary since it uses the same input ingredients as baking bread (grain and water) so I don't see the point of doing it.

Also, a few guides that I read have suggested that fishing is not efficient either, and I can somewhat agree with that after the beginning of a game since fisheries run out quickly and need to be rebuilt elsewhere.

So by only producing bread and no other food, we can never lose more than 2 pieces of food in a single mine, which effectively reduces the waste without the micromanagement of destroying them right away when they are empty.