The correct procedure involves removing the whole silver Amalgam in as big of a piece as possible; you definetely don't want them grinding them away as inhaling the vapor will often times be worse than leaving Amalgam in mouth. They usually use a rubber dam to prevent any pieces from being dispersed and ingested and a cold water stream jet to minimize vaporization; they should also provide external source of oxygen to reduce any chances of breathing in mercury. After the silver filling is fully removed they might grind a bit of the tooth if there are any tatoos present (where mercury leached out to the tooth).
Mike

A regular dentist will leave part of the amalgam.

A "Metal-free", "Biological" or "Natural" dentists will and should remove all of the metal before putting anything else in the tooth. Because Amalgams shrink and there is a small crevice or gap that liguids can get into and cause decay.

Elaine