Unless we're talking about a horror movie, it's not often that a title refers to a sharp tool that's used to carve someone's head into two bloody lumps—but Sling Blade isn't your average movie.
The sling blade is the weapon Karl uses to murder his mother and her lover. Here is Karl himself describing it to us:
KARL: Some folks call it a sling blade, I call it a kaiser blade. It's got a long wood handle, kinda like a ax-handle. With a long blade on it, shaped kinda like a bananer. Mm-hmm. Sharp on one edge, and dull on the other. It's what the highwayboys use to cut down weeds and what-not.
There is a lot to unpack when it comes to this simple tool. Like the sling blade itself, Karl can be seen as sharp on one edge and dull on the other. It depends on how you look at him. He looks simple on the outside, but inside, he is rife with inner conflict and turmoil.
On top of that, think about Karl's description of the sling blade as something used to cut down weeds. Well, Karl used this thing to cut down his mother, who he saw as a weed—useless, out of control, and destructive. It's how he views the villains his life later in the film, too. He sees his father as worthy of extermination, but after visiting him, he realizes the guy will just die naturally. Doyle, on the other hand, is a weed that's still growing. Doyle needs to be pulled.
Finally, the fact that the tool has two names shows us how two people can see the exact same thing and call it by two different names. That speaks to the ambiguity of the film, and how you can interpret it in so many ways. Unless, of course, the sling blade is rapidly speeding toward your face, in which case there is only has one interpretation: your certain death.