After an ectopic pregnancy they most likely would dispose of it in hazardous waste (the red trash bin). If you take the medication to dissolve the pregnancy it would most likely be dissolved or partially come out into your toilet when you use the restroom. Ectopic pregnancies usually need to be handled before week 8 if memory serves me right so they are very, very tiny.
It is illegal to just throw a body away and the hospital is required to dispose of the remains in a humane way. Typically they will do cremation or burial if that is what is wanted, but it is up to the hospital for what is done.
Dispose of it, but I'm not sure in what manner. I know some hospital have incinerators and use those for it, but you would need to check with the place and see their own ways.