Your plan sounds fine. Using a circular saw with a diamond blade will give you a cleaner cut. You can get by with masonry blades for the circular saw, but you will go through 2-3 blades and the cut wont be as clean. The diamond blade is well worth the investment, imo. You can have a helper with a shop vac/fine particulates filter follow behind to catch most of the dust as you are sawing, or you can have a helper use a hose or garden type sprayer keep ahead of your saw cut keeping the area wet. That's a tad more messier though. You wont be able to wet cut with masonry blades, just the diamond. With any method, use safety glasses and a quality dust mask as even when wet cutting, there is still dust.

When removing the existing framing on the inside but still keeping the stucco intact on the outside, use a reciprocal saw to cut the fasteners that are holding the lath wire to the studs. With a little patience getting those fasteners as well as the flashings below cutting from the inside, you can then reframe for the doors r.o. and cut the stucco out just before the door install as you have planned. Whenever possible on projects like this, it's best to work from the inside out as you have planned. You can also put up some plastic sheeting on the inside and make a closed off work area to keep dust to a minimum inside the house. I usually use push pins to attach the plastic to the ceiling and weigh down the bottom with lightweight lath boards or light scraps. Tape the plastic to the walls either side of the new opening with paint sensitive tape and give yourself plenty of work room. This is all assuming you have enough area to do this by simply making a tent around the work area.

Thanks for the advice everyone. A follow-up question... I haven't seen the door yet (arrives in a couple of days), but I assume there will be some sort of flashing, at least at the top, that is supposed to go underneath the stucco. Will this work with my current plan? Do doors like this typically have flashing for the exterior wall that's supposed to go under the stucco or siding?

Thanks again.

C

It's going to depend on the door. You are going to want to cut the stucco back enough each side and top if the door has a nailing flange to fasten into the trimmer/jack studs as well as on the header. The void can be filled with foam,(low expanding foam for doors and windows), befoe your trim is installed. The trim itself should be back caulked as well as topically caulked after it is installed. I would prime the trim all 4 sides before installing. If the door has no flange, you can cut the stucco tight, install the door, foam the gap, then the primered, back cualked, topical caulked trim. I dont normally recommend relying on caulk to keep water out, but seems like the only re-course without disturbing the stucco and trimming over.

The bulletproof way would be to knock the stucco back wide enough to run a head flashing over stucco mould that would trim out the doors exterior. The flashing would run over the moulding. Then self adhering bitumen type flashing installs up the sides with a piece then installed over the header flaashing. Then mesh wire/weep screed at the base followed by your stucco patching.Your scratch coat can be followed by the brown coat after 24 hrs and then let set a couple of weeks before the color coat. Your brown coat will be leveled with the existing wall surface. Grind enough of the existing top coat around the perimeter to be able to feather the new top coat into the existing. Depending on wether you have a textured top coat existing, or fairly smooth, i typically have exterior acrylic latex paint matched up to the color coat and paint the new color coat area as it is usually hard to match up existing color coats that have been on the home even if you knew the product brand that was used. That way you dont have to mess with trying to match up the color coat old vs. new. You would want an exterior flat paint.