The toxicity is in the GREEN parts of the plant...
“Green skin or flesh on a potato or sprouts from the eyes that dimple its skin signal rising levels of solamine that accompany the growth of a new plant.”
https://homeguides.sfgate.com/parts-potato-plants-poisonous-56644.html
That’s called a “slip”. Throw that in the dirt and you’ll make moar potatoes.
Yeah, I always cut off green parts. Articles says there’s a tiny bit of solanin or whatever it is in the tater itself, but destroyed with cooking. No one eats raw taters so no worries.