You could cut it up, but then you'd have to wait a few years for it to dry. I know becuse there has been slab of sycamore in my shed for ages now and it's still wetter than Peewee Herman in the shower.
I'm not actually sure (well infact I don't actually know) if walnut would be suitable for a neck. I don't know if it's stable enough and I think the & versions of the tree are different anyway.
I did find that neck laminates were suprisingly cheap. If you use a couple of maple laminates on the outside and some other suitable wood in the middle, you should be able to pick it up quite easy.
I also found that once you stop worrying about it and just get on with it, shaping a neck wasn't too hard, you've just got to be careful
Good luck dude.
Oh yeah, still chop the tree up and leave it in the shed to dry. That way in a few years you'll have some lovely wood (you might need to wax the endgrain of walnut to make sure it doesn't go funky though)