Several people have talked about having single edge knife so that you can cut down small trees. What is the proper way to cut or carve wood with a knife?
You really want a saw or camp axe for this purpose, but if using a knife you want one without serrations. Serrations are not a replacement for a saw. A saw cuts a kerf wider than the blade itself so it (with skill) doesn't jam. Serrations are usually placed near the handle which is exactly where you don't want them because this is where you have the most leverage for a push cut.
Getting onto technique itself, here are a couple of videos that show how to use a small knife (not a chopper) better than I could in words. If you have a proper fixed-bade you can use batoning which is a very powerful technique, but don't try it with a folder. (If you do have to use it with a folder, such as splitting wood in an emergency, unlock the handle a small angle so that each hit is not destroying the lock. This is dangerous and should not normally be attempted.)
Ray Mears - using a knife part 1 (knife skill starts 5 minutes in)
Ray Mears - using a knife part 2 (continues a minute or two into this video)
The start of this second video shows transverse batoning, the method that one would use to cut thicker or hard limbs with a small but sturdy fixed-blade knife.
Thinner and softer shoots and saplings can often be cut by bending the limb to pretension it, then cutting at an angle into the convex side. Be careful because you are cutting into what is effectively a spring.
What you want to do is find a good knife, that is partially serrated, so that you can have the choice of cutting things with the serrations or without...
I personally recommend the CRKT M16-10KZ (EDC) or another knife of the M16 line, as they cut small trees/shrubs quite easily. I've used the M16-10KZ (3" blade) to cut stuff like this before and it does it easily.
note: I am not affiliated with CRKT in any way, shape, or form.