drywallgaptexture
I am redoing my subbasement. Originally the inside corner where the wall meets the ceiling was not taped and jointed. Some floor trim was used as a poor man's version of crown molding, and it is hideous. 
I am taking down the trim and wanting to fill in the gaps where the joints were not properly done. Both the wall and the ceiling have been textured. Is there a way to properly do the joint without having the scrape off the texture?
I don't know that replacing the drywall for that little a space wouldn't be the best route. Seems the cleanest. Removing trim isn't hard. I don't know about the mirrors, though. Renting a drywall jack is cheap and makes it a ton easier to hang. A bit of demo and hanging a new ceiling sounds easier than messing around with something that isn't working out.
Beyond that, I don't know about knockdown texture, but sanding down a ceiling without a drywall sander sounds like it sucks and trying to water/scrape it sounds like it sucks and is super messy. Demoing drywall is quick.
No expert here. I'd just replace it. Seems the surest, which is the direction I like to steer.
Here's a few options I can think of.
If the wood is a bit thicker than the drywall, you could use a router to remove some of the material on the back side of the lowest plank (may require installing an additional plank, or extending the drywall). Then allow the lowest plank to lap over the drywall. Make sure you leave enough of a gap between the two materials, to allow for expansion and contraction.
Another option would be to use a transition strip, like the ones commonly used in flooring. You'd use T-molding if the materials are even with each other, or a reducer if they're not.
A simple 1x4 like the previous owners had, or a more decorative piece of molding could be used.
Best Answer
Or you can caulk the joints and smooth it out. Use a caulk you can paint over when dry.