I started a thread asking about how much weight people would dedicate to cutting tools. The Leatherman Micra and Victorinox Classic were mentioned quite a bit. We never really get down to ounces/grams.
Here are some options I have used:
Single edged razor blades: I pack one or two in my survival kit or first aid kit. I wrap them in clear shipping tape and trim it as much as I can. The tape keeps the blade clean and rust free and safe to pack.
If you want a nice light knife for general cutting and kitchen chores, consider the Victorinox stainless serrated paring knives. IIRC, they weigh 3/4oz and cost about $4.
For more of a "real" knife, the Swedish mora knives are excellent and quite inexpensive. You can get a 4" stainless blade knife with a plastic sheath for $10-$12 and they weigh 3-4oz with a sheath.
The Boker Trance is an excellent folding knife for general cutting. I carry one every day as my pocket knife.
The Swiss Army knives cover a wide range of size, weight and cost. In general, the simpler the knife is, the easier it will be to use. My personal preference is to the 111mm models, with the Trekker being my favorite, but it does stray from a truely ultralight tool. The long blade, saw, and the prying ability of the locking screwdriver make for a realistic survival tool.
I went through a search for a knife that also had scissors and found myself caught up in a lot of compromises trying to get an all-in-one tool. As mentioned in the article, small scissors can be found and I'll add that separate scissors are much easier to use. I opted for some Fiskars embroidery scissors that are under an ounce and have sharp tips. $3 at my local flea market :)
The really small light fixed blade knives are found listed as neck knives. There is a long standing tradition of small knives carried in sheaths on a neck lanyard. The Buck Hartsook is an UL hiker's knife-- 1/2 oz and made of S30V steel, which is quite hard and will take a razor edge. AG Russell offers the Woodswalker knife with a Kydex plastic neck sheath that is pretty much a paring knife with a good handle.
If you want to buy the folding razors one at a time, check out County Comm http://www.countycomm.com/straightrazor.htm
County Comm aslo has a hacksaw of the same dimensions as the razor and and excellent LED micro lights for $1.
If you want a saw for hiking, the Gerber/Fiskar Sportsman's saw is about 3oz and cuts very well. Wire saws are good survival tools, provided you get a good one. http://www.bestglide.com/Wire_Saw_Info.html has one of the better ones.
IMHO, a saw is only necessary as a survival tool for fire and shelter building and runs against any concept of leave no trace.
Most of the heavier cutting tools are survival equipment more than general hiking tools. As many have said, most cutting chores involve cooking or grooming, so a Leatherman Micra or a Victorinox Classic is about as much you would need for that. I equate cutting tools with first aid kits as both end up being a risk/weight consideration. For me, essentials are my largest divergence from the UL gear lists I see. I carry a first aid kit that is about 6 ounces and prefer knives that end up being more like 3-4 ounces. Much of this is driven by the fact that I usually hike solo.
It all really centers around a concept that Ray Jardine wrote about: many of the controversial issues with ultralight equipment come down to a fear of nature. The trick is to learn to live within nature rather than seeing it as an adversary. In reality that means understanding the physics and physiology of hiking, good preparation, navigation skills, back-up plans (like leaving your destination and return time with a trusted contact), and stringent equipment selection.