A saw can be a really handy thing to have in the woods. You can use a hatchet and a knife for a lot of stuff, but there are some things that a saw just does better. There are many different kinds of survival type saws ranging from the very small to the fairly large. I always, repeat, always have a saw with me. In the woods, at work, at the grocery store; I have a saw with me. Now you may thing that I look like a real wingnut carrying a saw everywhere, but the fact is it's not even noticeable. You see, I'm talking about the saw blade on my Swiss Army Knife. It's small, but it is so very, very useful. I use my saw to cut arrow shafts, I use it to cut bamboo for bundle bows, I use it to cut the nocks in arrow shafts, I use it cut out bone needles and fish hooks, and many other things. Here are a few of the different kinds of survival saws that are available today:
As mentioned above there are several different kinds of small saws that can be carried in you pocket at all times. Several models of the Swiss Army Knife, and similar type knives, have a saw blade attached that is very useful for small jobs. Many multi-tools have saw blades. Be aware that the quality and functionality of these blades vary widely. The Swiss Army knife, for example, has a good quality blade made of good steel. The blade also functions smoothly without binding up in the cut. I have a less expensive copy of a Swiss knife that does not work well at all. The steel is good enough but the spine of the blade is wider than the cutting edge. This causes the blade to bind after you have cut a little way through a limb. I would suggest that you spend the extra money and get the real thing. Multi-tool saw blades also vary widely in quality. I have a Leatherman that works quite well, but I have seen others that are not so good. Pictured below: Swiss Army Knife and Leatherman Multi-Tool
I keep a little wire saw in my survival kit. A wire saw is basically a piece of flexible, heavy gauge wire that has serrations in it. The wire has a metal ring attached to each end where you can grip the ends and saw back and forth with the wire. I have cut down some fairly good sized trees with a wire saw, maybe eight inches in diameter. I have also had wire saws break while in use, so I wouldn't say they are intended for any kind of regular or long-term use. One thing I can tell you from experience is to not try and use a wire saw by sticking you fingers through the rings. This is very tough on the fingers. the best way to use a wire saw is to get a couple of sticks that will fit through the rings and then grip the sticks. Much easier on the fingers. Pictured below: wire saw
Folding saws work very well but they are not convenient to carry. They generally need to be carried in a belt holster or inside of a pack. They are also relatively heavy compared to the saws mentioned above. The only time I carry a folding saw is when I know I will need it for a specific task. For example, if I am going out into the woods to cut some saplings or to work on one of my trails, I'll carry my folding saw. Otherwise it stays in my truck. Pictured below: folding saw
There are several different types of non-folding saws that can be carried in a sheath on your belt. I don't personally own one of these because it's not something that I would carry. It might work for you if you use a saw a lot.
Survival Saws as a Component of Another Tool
Some sheath knives and machetes have saw teeth cut into their spines. If a sheath knife or a machete is something that you carry anyway, why not make it multi-purpose by having a saw blade on it. The Southern Forest that I live in becomes very dense in the summer; almost like a tropical jungle. In the summer I always carry a machete when I'm in the woods. I used a file to cut saw teeth into the spine of my machete so that it can double as a saw. Pictured below: Two views of my machete with homemade saw blade
I have a couple of little folding shovels that have saw teeth on one side of the blade. I never carry a shovel unless I know specifically that I will need it, so the saws rarely get used. Neither of the ones I have are very good as saws, but then again they are not the highest quality shovels that you can buy. Pictured below: Folding shovel with saw-tooth edge
In summary, I think that the most practical survival saws are the saw blade on a folding knife or multi-tool, the wire saw, or the saw-tooth back of a sheath knife. Other types of survival saws are functional but not particularly convenient to carry.