Plaster of Paris can be cut on a milling machine or router. It's a bit dusty, but it's soft enough that it won't dull tooling too much. I don't know where to send you for data or standards on this, but it's not too hard to design a test part and try it.
There used to be a product called Rayite sold by USG as a machinable plaster. I tried it, and found that if I didn't let it dry thoroughly before cutting it the chips would stick to everything and make a mess. But when it was dry it made less dust than regular set plaster. My guess is that it was just regular plaster with a little PVA added for cohesiveness.
Machining ceramics is another thing entirely. Green (unfired) ceramic machines easily, but it's hard to hold onto, while the dust is both toxic and abrasive, so you'd need to protect the sliding parts of your machine (as well as your lungs) if you're experimenting with it. Fired ceramic can be machined as well, but it's difficult and slow, requiring special diamond tooling.