dd (now 16) who is NT used to have a thing about scribbling on walls and "defacing" things when she got angry an upset at that age, and younger. She used to throw things down the stairs (mostly laundry). I now think that finding a way to let off steam which isn't a source of shame is actually quite important, because as you say the mess upsets them and the feeling of having done something wrong.
For us what helped was not really worrying about the wall scribbling just going with it for a few years, reducing stuff in her room to a manageable level, lots of cushions and very large soft toys, and well...working on the anger so she didn't feel the need to throw stuff. But she was always going to want to wrestle with things and scribble, that was a bit of sensory necessity for her, and no amount of telling her off was going to help.
Lots of hugs, lots of nests, low expectations for her room being particularly smart, but tidying it regularily, lots of busy stuff for her do with her hands which wasn't too fiddly, and lots of physical outlets outdoors, dd liked skating, skateboarding, swimming, dancing (streetdance) being sat on, sliding down stairs, rolling down banks.
She also was constantly wanting to change her room, I think she was very disatisfied and got very overwhelmed by stuff, but didn't quite know what to do with that disatisfaction. I wish at the time I had understood that she needed perhaps a big foam chair, more storage and less decorations/bits. When they are 10 you are imagining a typical girl's room, but sometimes they need something more functional. But they don't know what they want, and start demanding things that aren't quite the panacea that they think it will be.
Also, might your dd be interested in construction activities, where she can do more taking things apart and rebuilding that is in a more positive free way, no repercussions? Not lego but perhaps papermache or clay modelling.