Lately, next to my flower in its pot, mushroom is growing.
Why? What should I do to stop the mushroom from growing?
It was written on Google that the fungus causes the death of this flower
Nothing to worry about and you can't stop the mushroom/s from growing, though you can just remove it yourself. Mushrooms are just the fruiting bodies of mycelium present in the soil - you may find they recur at the same time next year. As for 'killing your flower', if that's what Mr Google said, then he cannot be trusted on this subject - it won't kill your plant, although we don't actually know what plant you're growing. The majority of mushrooms feed off dead material, not live plants, they are part of nature's recycling/disposal system.
The mushroom itself is almost certainly not an issue (other than possibly aesthetically). Almost all species of mushroom are saprotrophic, which means they feed on decaying organic matter (and are a key part of the process of decomposition). Very few species are active parasites of live plants, and a vast majority of those that are only parasitize woody plants, and that would be about the only way it’s likely to kill your houseplant.
That said, the presence of mushrooms in the pot is possibly a symptom of some other issue that may kill the plant. The most likely possibility is that you’re watering it too much. Most mushrooms require a significantly higher level of moisture in the soil than most plants do, so they only tend to show up in over-watered pots.
To confirm that, as other answers have suggested, this specific mushroom is harmless - this mushroom looks to be a member of the family Psathyrellaceae, perhaps even Coprinopsis atramentaria, the Inky Cap. Watch over the next few days to see if the cap starts to dissolve into a black, inky liquid. These are among the saprotrophic fungi mentioned by Austin Hemmelgarn, meaning they will not parasitize houseplants. Neither will they form symbioses with houseplants, for that matter. What they will do is help make nutrients in the soil available for the plant to use.
(obviously, do not eat any mushroom based on identification by a stranger online)