Sometimes removing teeth becomes a little more complex. Teeth that are very decayed or have been heavily filled/crowned or have badly broken have to be removed surgically. This sounds awful - in fact it is a very similar sensation to having a filling. If you are squeamish, do not read the next paragraph - it will just put you off!
The thing you need to know is that the dentist will make sure it is really numb, so you shouldn't feel anything other than some pushing. The whole area is made really numb, a flap of gum raised around the tooth is lifted away and some of the bone which is holding the tooth in, is removed. Sometimes it is necessary to divide the tooth into pieces. The tooth is then removed and the gum stitched back into place.
Sometimes your dentist may refer you to an Oral Surgeon for this procedure.