"Your" cutting table, is it your own place in the room, or a shared space? If it's yours alone, then leave your work out on it.
If he can't be bothered to clean up after himself, let him know you'll just sweep everything off towards his side of the room. Yes, it will likely damage his work and his supplies a few times.
Or make it a rule that he doesn't eat the next meal (of you cook and serve them) or go to bed until he removes his stuff. At least that way, it'll only clutter up the table for a few hours at most, not days. This isn't harsh punishment. It shouldn't take him more than a few minutes to move things. It's not that he has to put everything away neatly, he just has to get it out of your space. It's no worse than reminding the kids to wash before eating or brush their teeth before bed.
As for the woodworking project, there are two solutions to problems like that. If he needs to leave it there to dry, he can ask your permission, just so he moves it once it's dry. Or he can do the work downstairs and haul it up to his office to dry.