Is Removal Of Placenta Followed By Abortion Pill Intake The Right Procedure For Abortion?

Hi. I m having an abortion this weekend. I m approx 13-14 weeks pregnant. The doctor has explained that she will first put the pills In my vagina and let the foetus come out thru contractions and bleeding and will then perform removal of placenta whilst I m on anesthesia. I just want to confirm this is the right way and will I not feel anything during the placenta removal due to anesthesia?