Yes you are allowed to keep your amputated body parts and bring the amputated body parts home from the hospital.
If you are able to tell the doctor or surgeon that you want to keep your amputated body part they can help you preserve the amputated body part so that you can bring it home.
The doctor or hospital staff should also fill out a form that shows that it's your amputated body part so that you don't get into trouble.
But you are allowed to keep your own body parts at home or wherever you want to keep them.
Otherwise the hospital just disposes of the amputated body part someway.
I'm not sure how they do it but they likely either grind it up or throw it in a furnace to cremate it.