for hard copper, flow Ni thru it and anneal it, cool it. it is now soft copper at that location. have done that w/ 1 1/2 pipe that I needed an offset in. saved two 45s and four braze joints.
For that composition cut, I'd cut thru the stucco, then switch to wood bit as well.
As far as the wood hole sawing- drill several holes w/ spade bit thru where the cut of hole saw will be. this gives a place for the chips to drop out kerf (slot cut by saw), otherwise the chips clog the space between the teeth (fillets) and prevent efficient drilling. really helps w/pine or other pitchy woods.
For bigger dia holes, i use a sawsall/ recrip saw and use the spade bat as pilot hole
Col 3:23
questions asked, answers received, ignorance abated