The question is obviously (to me, being OCD about this kind of thing myself) a matter of removing the evidence after digging them out. (40D's channelling without ramps was nice for these visuals. Also for defence. Of course, there's something to be said with the current method, and I've adapted accordingly.)
There really isn't (at the moment) a way to make it 'clean', unless you have a lower exit that you can wall off (can be disguised among other smoothed walls, if not in soil). There might be an option to obsidian-cast over it as well, but I've never gone that far, myself.
Alternately, it might be a question about defensibility, in which case you can (like I do) leave ramps down from the outside of a ditch, except (mostly for the visuals, not practically different in any other manner) where a draw bridge lowers to let the externally-exiting internal-ramp-derampers back 'inside' the enclosure.
If it's a particularly deep cutting, I'll often leave an 'island' in the middle of the mutli-tile-wide channel with a ramp Z+1 up from the bottom onto a pillar (often, itself, a number of Zs below original ground level), and a drawbridge connecting that refuge with an entry/exit in the wall of that channel. Then the miners (and bone-collectors, if your enemies are going be plummeting down) can enter and exit at your will without there being a vulnerable path always open. (It would be even be [CONSTRUCTION_DESTROYER:2]-proof, if such a designation actually existed. Leastwise the non-flying possessors of that tag.
)
A further alternative: exit
down below the bed of the ditch, and out through a U-bend, with a bridge to cover it (and another at the inner side, for security?). A bit of planning is needed to make sure there's another ingress/egress there for the mechanic connecting up the "open this" mechanisms in order to make the gap passable again, but this temporary access can then be removed/disassembled with the bridge 'open'. Make a feature of it! Connect it to a water(/magma)-drain, if you're flooding the channels! You could at least prepare for the possibility, even if you're not going to do it straight away.
A visually stunning method, though, might be to make the walls of the channel totally stairwells (like those empty dwarven mountainhomes, you get (got?) to see in Adventure Mode. And then, when you're happy with the channel (or earlier, if you don't need one particular side to access the construction/destruction zone) just floor over the ground-level (or equivalent) down-stairs to stop all access (and exit).
Some of these need more work, some
virtually no more than just leaving the miners in the bottom.