What type of window is this and how can I remove it with minimal damage to the wall?
You have about a depth of about 5/8" to 3/4" of material to remove back about 1 1/4" from the frame you see protruding from the wall. 

The aluminum nailing fin is about 1/8" thick and 1" to 1 1/8" wide.



I was lucky in that the base on the DeWalt cordless saw I used spaced the blade the perfect distance from the aluminum frame as a cutting guide. I used a carbide blade, set to depth, cut a strip out all round the window and then finished cutting the corners out with a chisel. This was on wood siding, Stucco, being cement will require some sort of masonry blade and dealing with the heat involved cutting through.

After pulling the nails out of the fin, the window dropped out. Follow directions for reinstallation, there should be a special section for stucco. There are other questions asked on DIY here for Stucco repair which will be the next hurdle.