The worst case scenario is that that section has died. If that is the case, the dead trunk can be removed at the point where the two trunks divide...but not below that. Was this a sudden occurrence or a gradual die back?
I'd probably leave it until spring and see what leafs out before you cut anything. Most of my JM's look horrible and ratty by this time of year--out here they don't tend to put on a nice show of fall color like they do in other parts of the country, the leaves tend to just brown up and die and eventually fall off (although on some of mine, I have to run my hands down the branches to get the dead leaves to fall off, otherwise I think they'd stay on the tree all winter). In the spring if that half of the tree doesn't leaf out then it's dead and you can prune it out, but you may be pleasantly surprised.
Japanese Maples look pretty ratty by about August and if they are in full sun or exposed to the wind in Sacramento, I am not surprised it looks dead.
Scrape a little bark away from one of the smaller twigs and see if it is green or sort of moist. If it is obviously tan and dry, then cut off that part. Keep testing farther and farther down to see where it might still be alive.
Waiting until the buds swell is a very good way to tell, too.
I agree with the others who suggest waiting till new growth come spring, once that new growth is visable, it will show you IF the part that looks dead now is still not leafing up by end of June say, then you can check again by doing a small gentle rubbing of one or two twiggy shoots to see of under the bark there is live tissue or brown wood, the latter is dead wood and that indicates the branches are dead but IF white /green or fleshy coloured, then that area is alive and will show new growth soon.
To Take extra precautions at this time, I would gather up and burn ALL the fallen leaves from this tree in-case there is a disease lurking within the tissue, this clean-up will prevent the spread further as some diseases can lay dormant over winter, I would also dispose of the leaf fall either by burning or removal from the garden, burning is best as it prevents spread elsewhere.
Good luck. WeeNel.