Cutting with a saw it's absolutely Ok, but of course, it depends on the size of the branch / trunk.
You can also use a concave cutter called "Ryuga", those are designed specifically for bonsai. The fact of "carving" the wood helps to close better the wound.
It's always better to cut in angle, and if it has a branch just by the side even better.
Sometimes you will have to be careful, specially on maples, because when you cut they tend to dry the branch.... I don't know exacly how to explain this in english. But you should leave a bit more of the branch you want to cut.
As an example here is my maple.
![20210514_212150.jpg 20210514_212150.jpg](https://www.bonsainut.com/data/attachments/363/363835-85ed58dddcfd4898ca62667e9e92e7a7.jpg?hash=he1Y3dz9SJ)
First I cutted leaving an extra chunk that will dry out, and then I will cut again safely.
And if it's a big cutting always seal the wound. Again, there are lots of products.
The most important is that the wound is sealed so it won't get deseases.
You can use sealing paste or even wood glue.