Yes. I didn't look at your image (forgive me) but you can channel out a large square volume of stone for a courtyard entrance (I did the same thing for a fort) easily with a cave-in.
Step 1: Designate it with Dig on all levels you wish to clear, and make sure there is access for your dwarves to dig it.
Step 2: At the second-highest level, place a support near the center of the area.
Step 3: build a lever in a safe place (not where the stone will fall) and attach it to the support.
Step 4: At the highest level, channel out the area immediately surrounding the are you intend to drop (it should then be suspended and resting on the lever).
Step 5: Get everyone the heck out of the way, and Pull the Lever. The cave-in will fall all the way down through the entire courtyard, clearing all of the floors beneath it.
Notes: Of course if the area of the top level is irregularly shaped, you may need to repeat this process with multiple cave-ins to clear the floors on all levels. Alternately you can choose to cave in the highest square covering a large area, then channel out whatever remains.
Also, you can avoid digging out one level and the cave-in will stop there. In this way you can use the first level of the courtyard and not worry about 2000tons of stone coming down on your dwarves' heads when you pull the lever. Or, you can clear the courtyard, draw enemies into it, and pull the lever for a lot of fun.