Course we do. We do it all. And there are a lot of knives on the market designed for exactly that.
Which means that they are, at best a compromise.
I am talking about batoning. Of course, the tool of choice is an axe or hatchet if you want to split wood. Even better, a froe. If you have none, you always risk breaking your belt knife, which really sucks. Or you carry around a froe with a tip and a different handle, aka Survival knife. You can find some which are really great cutters, too, no argument necessary. But fact is, batoning puts a lot of stress on a blade.
This is how I like to do it.
Gently tap the spine of the knife so that a crack opens.
Whittle a glut or wedge.
With a controlled motion, using one hand to keep the wedge in the crack, turn it towards the top.
Split the branch with the wedge.
Now you have two halves, e.g for whittling a spoon. 
