What is the ruling on amputating a specific limb of a person, such as a finger, etc. Should it be thrown out with the garbage, or should they be collected and someone appointed to bury them in the Muslim graveyard?

Praise be to Allaah. 

This matter is open, because amputated limbs do not come under the
same ruling as the whole person. There is no reason why they should
not be put with the garbage, but burying them in the ground out of respect
towards them is preferable. But the matter is open, praise be to Allaah,
as we said. They do not have to be washed (ghusl) and buried unless it is a foetus of more than four months’ gestation. But if it was merely flesh into which the soul had not yet been breathed, or it was an amputated finger or something similar, then the matter is open. But burying it in the ground is good and is preferable.