Both of the above post have very good points.
For volume removal try this only if the stucco is on metal lath.
Use scaffold only for this method make sure it is TIED OFF.
Start by removeing a section between studs using the saw method cut vertical between studs from bottom to top and horizonal at the top gravity should assist you at this point. Keep in mind stucco weight is approximately 8 to 12 pounds per Sq/Ft.
After this section is removed start at the top of the exposed studs prying the fasteners loose or use a sawsall to cut the fasteners,pry the stucco back to reach the next stud and repeat gravity will again assist you. Another tool to help is a good SDS drill used on hammer only with a wide spade bit to work between the studs and stucco.
Make sure you protect everythinh below working area.
As for replacementit may depend on what type substrate you have under the existing stucco.If you have to add sheathing over studs plus Synthetic stucco system you will be bumping out 1 3/4 inches this will affect your trim.If you select synthetic check with your termite bonding company as to what affect it may have on the bond.Go back with conventional stucco an contract with a good company that does stucco.
You may also think about having them do the removal.