There are many electrical saws that don’t cut into wood with a rotating circular blade and use another method of cutting instead. Here are several of them:
The Bandsaw
The bandsaw often has a place of choice in woodworking workshops—and for good reason. It is an unparalleled tool to cut wood into curved or irregular shapes with a high degree of precision.
Moreover, the bandsaw can resaw lumber in a way that minimizes the loss of material since its blades are thin compared to the ones of a table saw, for example.
Also, it is a tool that is very safe to use as long as basic security procedures are respected.
A bandsaw works in a relatively simple way. The blade of a bandsaw is a flexible hoop made out of thin metal and that has teeth on one of its sides. The bandsaw has two wheels on which the blade runs just like a belt. The blade is tensioned enough so it doesn’t go off the wheels and cuts correctly. The bottom wheel of the bandsaw is coupled to a motor and makes the blade turn around. By moving this way, the blade makes the top wheel turn at the same speed as the bottom wheel.
This motion allows for a section of the blade to move constantly downward. This is the section that is exposed and that is used for cutting with a bandsaw. The tool is conceived in such a way that the blade goes through a table on which the stock to be cut rests on.

The bandsaw is a safe tool to use because of, among other things, this constant downward motion. This motion means that even if the blade gets stuck in the workpiece, the workpiece will be pushed downward but still won’t move this way since it is supported by the table. This means that this situation is generally not very dangerous, albeit not quite inoffensive. In addition, this kind of jamming can break the blade or damage the bandsaw. Still, it is much better for a bandsaw blade to jam than for circular saw blade to do the same, since it then the tool has good chances of being propelled in an uncontrollable fashion. Unfortunately, many fingers have been lost this way.
Metal cutting bandsaws also exist and metal cutting blades can’t be used on a wood-cutting bandsaw. This is because cutting metal requires a much lower speed than what wood bandsaws run at.
The Jigsaw
The jigsaw is also a relatively safe to use. It is a versatile power tool since it can make straight cuts, curved cuts and make openings in the middle of a piece of stock. It can be used on wood but also on a variety of other materials like metal, plastic or even cork and leather as long as the appropriate blade is used.
That being said, the tool does have one weakness: it is harder to get good straight cuts with a jigsaw than with a circular saw (skilsaw).

The jigsaw has a shoe that slides on the material during the cut. Its blade cuts through stock by going up and down repeatedly.
It is often one of the first tools that people recommend for a beginning handyman to acquire and I agree with this advice since the jigsaw allows to experience the cutting of wood or other stock without too much risk. Furthermore, some projects can be completed without any other cutting tool than a jigsaw. Then again, having other cutting tools wouldn’t be a luxury and a mitre saw, for example, could help a lot. This saw, while being more risky to use than a jigsaw, is still the safest saw equipped with a circular blade to use with the only exception, to my knowledge, of the SawStop table saws.
The scroll saw
The scroll saw is mainly used to cut curved or irregular shapes or to cut an opening inside a piece of wood.
This saw is often used for delicate and intricate work like marquetry. It can cut through a piece of lumber of a maximum width of about two inches (this capacity varies from a model to another).

The scroll saw has a table against which the piece of stock rests and slides on while it is being cut. The blades of a scroll saw, although they vary in size, are generally very thin when compared to other types of saws. The blade of this tool goes up and down very quickly, which allows it to cut through lumber.
This motion means the material cut on the scroll saw can have a tendency to “chatter,” which means to vibrate up and down to the rhythm of the blade movement. This weakness of the tool is usually at least partly corrected by a component called the drop foot, which is meant to hold the material to be cut against the table. That being said, a scroll saw I previously owned used another type of apparatus made out of plastic to hold the stock down: it wasn’t particularly effective, which is probably why it has rarely been used.
The oscillating motion of the blade also means that part of the saw dust produced during the cut is lifted on top of the stock being cut, which can reduce the visibility of the cut line. Scroll saws remedy to this problem with the help of a small hose that blows air on the cutting line. On the model I owned mentioned earlier this solution was not perfect either, but it surely works better on other scroll saws.
The Reciprocating Saw (Sawzall)
This saw can be especially useful to cut down assemblies, like wood pallets or an old patio for example, into pieces of lumber. When used for this kind of task, it has the undeniable advantage of being able to cut both wood and nails or screws when equipped with the appropriate blade. It can also be equipped with blades made for wood or for metal alone.
The reciprocating saw works in a relatively similar fashion to the jig saw. A straight blade having several teeth makes a fast and repetitive back and forth movement, cutting wood like a hand saw would. A component named the shoe goes around the blade. Most often it needs to be pressed against the stock being cut. Otherwise, a strong vibration has very good chances to be transmitted from the tool to the hands of the user. This is not very dangerous, but may be unpleasant and affect cut quality.

When the stock being cut is wood, this saw is often used freehand for jobs where precision isn’t all that important since other tools, like the circular saw for example, will generally do a better job at making accurate straight cuts. That being said, when cutting metal, for which the user often has fewer cutting tools at its disposition, a good enough degree of precision can be reached by meticulously using a reciprocating saw freehand.
The Oscillating Multi-Tool
This tool can be equipped with blades for wood or metal but also with scrapers or with sanding pads. It transmits a very fast oscillation to any accessory it is equipped with, which vibrate at high speed.
Among all the cutting tools mentioned in this article, this is the one that has the least cutting power by a large margin. It is not really used as a cutting tool for furniture making: even a pretty dull hand saw would do a better job for this application. That being said, when equipped with a sanding pad, it can be a useful woodworking tool since it is then able to sand hard-to-reach corners.

It does have its uses as a cutting tool, though, especially for some home improvement tasks. Indeed, what it doesn’t have in cutting power, it makes up for it by its versatility. The oscillating multi-tool can do plunge cuts in corners where any other tool mentioned here can’t be used. For example, when a moulding installed at the bottom of a wall must be cut into without being removed, the oscillating tool can prove to be of a great help.
This tool isn’t dangerous to use because of its limited cutting power. That being said, it tends to be loud and require the use of hearing protection just like most other power tools.
Commit your way to the Lord; trust in him and he will do this: He will make your righteous reward shine like the dawn, your vindication like the noonday sun. Psalm 37:5-6