Like u/Aww_Topsy explained, the mushroom is not the whole organism. It's just the fruiting body. The organism itself is the mycelium network. The mycelium network lives for a lot longer than the mushroom. I suppose a mushroom fruit body starts to die after it releases spore. Once it has completed its reproductive function it is no longer needed. Picked mushrooms are not dead. You can take tissue clones from store bought mushrooms and cultivate them. Mycelium networks die when another fungus or bacteria out competes them, or when they exhaust their food source.
EDIT: Potato grammar. Thanks u/AugurAuger
Mushrooms are the fruiting bodies, the “roots” would be the mycelium which is the “plant”. So when you ask when it dies, it’s like you’re asking when does an apple die.. it just spoils. The spore is the reproductive organs which can be found in gills of Agaricus bisporus, which is commonly used in cooking. The spores from the mushroom will create mycelium in the ground which may produce fruiting bodies - mushrooms.
Source - study Mycology
This is a very tricky question. There are no absolute scientific definitions for *alive* or *dead*, so this is really a philosophical question.
The general topic has been debated a lot. My favorite example, from The Infinite Monkey Cage podcast, uses a strawberry as an example.
Mushrooms are actually fairly physically hardy. People have even supposedly, managed to get mycelium to grow from dried mushrooms. It also depends on what you consider living, like when a humans heart stops are they dead? Or are they dead when every cell in they’re body is dead? Mushrooms being colonial and growing vegetatively, all it takes is a single dikaryon/2 spores(microscopic, 2 single cells) and a food source an an entire life cycle can be completed.
Depends on your definition. In a way, even a slab of raw meat is alive if your definition of "alive" is biological reactions to external stimuli, although vegetables are the most interesting example of this. Onions and potatoes the most, since the stinging vapors onions release are actually a natural defense mechanism, and if you were to cut a frozen onion there would be no release. Potatoes are interesting too because they're the only vegetable I know of that can't be refrigerated or frozen raw.
With mushrooms especially, it also really depends on the mushroom itself - some variants are extremely hardy and could be replanted whereas others are quite sensitive. The most true definition of death would probably be when it's spoiled too much for human consumption. Otherwise, it's still in fairly decent health.
On Food and Cooking: The Science and Lore of the Kitchen is a book that actually goes largely into the biology of food and how it changes at a biological level with various techniques and such. It's only slightly related, but it's a really cool book.