Start by looking at the top of a hill, grass and boulders and whatnot. Drop one level. Order ramps dug across the entire area you want to become empty space, right up to the final edges of the cliff. The ramps remove the floor, cause no cave-ins, and do not cause pathing difficulties like channels. Once that floor is completed, drop another Z level. Designate your empty space again, expanding the area skyward if the hill grows outward. Wash rinse repeat until you reach your intended ground floor. Designate to remove the ramps at the bottom edge of the cliff. Heaps of stone will lay around your new entryway. Build a single ramp and adjacent wall near a mason shop, designate an activity zone off the top off the wall as a garbage dump, use the new d-b-d combination and designate all that stone to be dumped, reclaim once its done, and there you have it. A hundred stone pieces sitting next to your mason and an enormous cliff face to build your gate into.
I'm currently using this method to carve underground streets six tiles wide and five or six tiles tall. For an ongoing project like that, dig chunks of street out with ramps starting at the top of the space and retreating one horizontal level from the long end of the street every Z level you go down. Working like this prevents cave-ins. I've made a very nice columned forum with two levels of balconies in front of the proposed palace site this way.