not all stones can be cut. you'll really want to have it looked at by someone who can tell you whether the stone is high enough quality to even be cut first.
if it's high quality, you probably could get it facetted. if it's got some internal cracks or inclusions, you might be able to get it cut into a cabochon. if it's got a lot of cracks, you might not be able to get it cut at all.
most of those pay-to-dig mines will offer stone cutting services, either on site or through the mail. do a google search for those types of places (i'm having trouble remembering any off the top of my head) and call 'em up to ask if you can mail them your stone
warning: expect to pay a very pretty penny for it, expect to wait a long time for it, and expect the stone you get back to look nothing like the one you sent and be very much smaller than you thought, especially if you're having it facetted.
sometimes, if you're lucky, you'll have a local rock hound club or lapidary club that you can contact whose members might be able to do it for you. their members are usually older and genuinely just love rocks, so they're not usually likely to rip you off.
you could also try contacting various rock shops (there's one in washington called jerry's rock and gem that i can vouch for personally) and see if they're able to cut rocks themselves or can send rocks to a reputable cutter.
hope this helps!