So like, construction materials? Will you need a lot of it? In production? One-offs?
There's kind of a gap there, probably, yeah. A stiff/dense urethane foam seems like the most direct comparison probably? As far as still non-cellulosic materials (i.e. excluding wood-fiber composites) go. Otherwise, you're looking at rather soft things like polystyrene/polyisocyanurate foams, or rather hard things like fiberglass and other composites. Or combinations of the two.
Which, fiberglass can be used a whole hell of a lot of ways; it's got good strength and stiffness, so can be made into thinner (webbed, flanged, truss, etc.) shapes better than a soft material can -- but at some effort, whether by machining down a block/sheet, or gluing pieces together (or "printing" over a form, as the CNC fiber methods, like carbon fiber fuselages). Or molded over a soft (foam) core, for excellent strength and stiffness and more resistance to buckling than the plain material. Or printing GF-reinforced resins, if that counts well enough.
And there's chop fiber or fabric, with resin, in a mold, an excellent way to make high performance free-form parts, but you need molds to do it -- good for production, bad for one-offs.
If you just want something you can (circular) saw apart and screw/nail together... yeah, I would suggest sticking with wood. Use wood-joinery methods with wood (imagine that
). Deal with the, whatever, flammability or temperature range limitations, that's about it. If you need other properties, you'll need other materials, with other cutting and joining methods, that's simply how it goes.
Tim