edit: Quintruple-ninjaed, but that's what you get for trying to be thorough. 
Plan a
head
At it's simplest, perhaps[1] you should only be channelling away floors that are not the last connection between some floors and the rest of the solid ground of the map.
As a demonstration, look at the following sequence, demonstrating two ways of what I sometimes do when trying to remove a square of floors.
A1) A2) A3) A4)
####### ####### ####### #######
####### ####### ####### #_____#
####### ####### #_____# # #
####### #_____# # # # #
####### ####### #_____# # #
####### ####### ####### #_____#
####### ####### ####### #######
B1) B2) B3) B4)
####### ####### ####### #######
####### #_###_# # ### # # ___ #
####### ##_#_## ## _ ## #_ _#
####### ###_### ##_ _## #_ _#
####### ##_#_## ## _ ## #_ _#
####### #_###_# # ### # # ___ #
####### ####### ####### #######
In the A example, as you can see from A2, I go straight across the middle (I could also do one edge, to later progress only in one direction, but this way there's roughly half the effort, the bigger the area). There's no way that any of those tiles would cause a problem, but (apart from the extreme left and right tiles) you probably don't want to risk these tiles still being unchanelled when you move on to stage A3, so you ensure that all the tiles are currently being worked upon before moving on. You might want to keeping an eye on things to make sure an over-zealous miner isn't working on one before a slovenly one finally wanders over and starts to work on one it was supporting, though. When A3 is complete (or nearly so) you can get A4 started, and that's as far as that one goes, but you could extend it.
When it's a square of known size, I'm quite fond of the B-series method. Initially, lay out a cross of channels to the full extent of the digging out. Note how the centre tile is supported by four tiles, the tip of a triangle coming out from each side. Once the cross-channels are cut, the four triangles are totally independent and in B3 you can see that I've started to shave the point off each one. In reality, you can actually designate each progressively larger edge as soon as the 'corners' of that edge are dug out (and there's no more central part to that overhang), asynchronously with any other edge. But I like how you can simple designate a square of channels, and this overlays only the floors that are the next to go. Also, when you get to stage B4 (or however big a square you're channelling out), you already have visual indicators to show that you've reached your pre-planned size, because there are no more channels to cut off a lip between.
If you find yourself with the need to remove more irregular versions, just progressively shave off any 1xN lips that you can find. It's possible that you could end up with a long run of floorway leading to something you need to cut... In the following example, do not try to channel away any of the tiles on the length upon which A is marked, nor should you probably channel away (without knowing what you're doing) both B and C together. The tile in the TR corner of the 2x2 encompassing these would not be supported by the 'edge' tile diagonally NE of it, nor the 'tongue' tile diagonally SW of it. There are several ways of getting rid of this overhang (although personally I would have tried to make sure that this shape never arose from the previous digging sequence), of which the simplest might be just to shave the three tiles at the easternmost extremity of the tongue (with the C centre-most), then the next three (with the B top-most), the next three, then make sure you remove the top/bottom tiles in the next row before you attempt to remove the middle one, then it's even more boringly intricate micro-management to remove each of these in sequence as you 'retreat' to the permanent edge, past A, which for the sake of argument I'm assuming is everywhere except for the long 'A' extension itself. But if you were also removing some of the outer tiles then there are quite a few that can be simultaneously assigned to be channelled which (even before the 'tongue' is removed) would not be adverse to the rest of the 'ground'.
#################
###### ##
#### ##B# #
#######A######C #
#### #### #
### #
## ##########
# ############
#################
Noting that the above may not be anything like your particular need, but are just there to demonstrate the principle. Remember that bridges do not support other tiles (constructed walls/floors/etc, natural w/f/e or other bridges), so don't use these to 'reach' the likes of A and assume that that cutting A away would leave a floor supported by the bridge.
I'm really assuming that you've already mined away beneath all these floors, of course. If you haven't, then they're supported by the solid tiles beneath. But these days if I'm removing significant amount of layers I tend to (r)amp on the level below (after checking for pesky trees on the surface level, which can cause cave ins). You can designate as far and as wide as you want, with ramps (assuming you're not forgetting about those trees, or other tiles that are effectively "Z+2" to the ramping designation, but otherwise unconnected with any other part of the world), and while it may create a hodge-podge of isolated ramp tiles in the middle of the expanse (and the obligatory ramps at the edges), those remaining ramps do not cause cave-in when fulfilling a new ramp-designation on the level below.
IYSWIM.
[1] Alternatively, a quicker way might be to engineer that there be a single floor tile connecting a whole lot of 'floating' floor, and then channel that away, but you'd be wise to ensure the digging is done from the solid-side (place a construction-to-be on the tile(s) you don't want to be stood upon, but then suspend them so that no pesky mason/etc goes there at the wrong time) if not also build a Support ("b", "S") to hold the floor up even when you do, but then (after making the appropriate link) pull a lever set at a safe place distant and see the whole thing collapse.
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Topic: Question on channeling (Read 472 times)