The Short Answer
No. Such a device is not plausible at any tech level as it does not obey the laws of physics.
More specifically, such a device violates conservation of momentum. Although it first appeared as a consequence of Newton's laws, conservation of momentum is extremely fundamental to physics. In fact, it can be shown using Noether's theorem that momentum will always be conserved if the laws of physics don't change from place to place. (Although the universe is perverse, it's not quite that bad.)
This means that momentum cannot be magnified or reflected; it can only be concentrated, diluted, or transferred. There are two points to note here:
- Force is a flow of momentum, in the same way that current is a flow of charge. Therefore, by definition, whenever the momentum of an object changes, it must have a force applied to it.
- Momentum is a vector. This means the total amount of momentum is conserved, including the direction. For example, two cars traveling at right angles with equal mass and speed have a net momentum that is at 45 degrees to their directions of motion, and that's the direction they'll go if they collide. But if it was a head-on collision, the total momentum would be zero.
Importantly, we can see that your device as described must violate conservation of momentum, even without knowing how it works. To do that, I'll make a slight change to the scenario and set it in space: that way, we don't have to worry about momentum being transferred to and from the Earth.
So, to set the scene, we have a truck bearing down on our kinetic knife (feel free to use the name!). Just before the moment of impact, we pull a curtain over the whole scene. After a second, we pull back the curtain. The knife is still floating where it was before, but the truck is now split into two neat pieces, each traveling at right angles to to the original direction of motion.
I'm making two assumptions here about how the kinetic knife works in your headspace:
"The device suffers no noticeable harm" means that no force is applied to the knife, or the amount of force experienced is much less than it would typically take to stop a truck.
"The vehicle's kinetic energy tears the vehicle in half in the direction of motion" means that somehow the forward motion of the truck is changed into sideways motion, in whole or in part.
I'll assume the more extreme end of both, as it makes it more clear what's going on, but the principle is the same no matter how small the effect is.
So, before the impact, the entire system (truck + knife) has some forward momentum. After the impact both the truck pieces and the knife are not moving forward, so the forward momentum is zero. Nothing is not something, and that's all there is to it. The effect, as described, cannot reconcile with conservation of momentum.
Focusing and Conducting Momentum
The description of the mechanism of action is totally plausible, if we make a small change:
[...] this device magnifies and concentrates [the flow of] momentum.
If the car slammed into a wall, as AndyD273 says, "all of the momentum is [dissipated] bringing the car to a stop." More accurately, the momentum flows (via a momentum current, i.e. a force) from the car to the wall. The wall doesn't start moving because it directs the momentum flow into the ground, where it is absorbed by the huge mass of the Earth.
The important thing to notice here is that the car loses all of its momentum when it comes to a stop, no matter what stopped it. We could replace "wall" with "kinetic knife" in the previous paragraph and it would be equally valid.
However, the force does not necessarily have to be the same. After all, the amount of force on your wheels during normal braking is far less than the force on your bumper in an accident. The difference is that a large force quickly transfers momentum out of the car, stopping it quickly, while a small force slowly draws momentum out of the car, so it takes a while to stop.
We can also change the pressure by distributing the force over different areas. Normally your car tires handle the weight (downward force) of your car just fine. However, if all that force is concentrated in the tip of a nail, the pressure goes from 40 psi to many thousands of psi, high enough for the nail to force its way into the tire and puncture it.
In fact, this is exactly the mechanism described. Let's take an ordinary knife as another example. It takes the force you apply to the handle and concentrates it into a tiny region along the edge of the blade, where momentum flows from the blade into the object.
Cutting a Car
Cutting a car in half presents some challenges. The metal of the car requires a very high pressure to cut. We must have a very sharp edge to minimize the amount of area, and therefore the amount of force it takes to cut the car. We also need a material that can handle higher pressures than the metal. Finally, we want to reduce the amount of friction between the blade and the car, so that we can minimize the amount of 'wasted' force we have to apply.
Right now these requirements are not met by any material. If we want to slice through the car as easily as a katana through cardboard we need something that is as hard, compared to the car. Your best bet is probably some sort of exotic energy-based blade. Note that lightsabers are typically depicted as several centimeters thick and melting rather than cutting, whereas your blade would be impossibly thin, a nanometer-thick sheet of energy that slips in between the atoms of your target, breaking the chemical bonds holding them together.
The actual minimum force it takes to split a material is limited by the material's surface energy. This paper gives a value of around 1 joule per square meter for aluminum. After multiplying by two (because a cut creates two surfaces), this is equal to around 2 ounces per linear foot. That is, it would take at least two ounces of force to cut through a foot-thick sheet of aluminum. That's not much, but it does mean that monofilament whips sometimes seen in science fiction wouldn't be able to cut through thick metal as they are just too light.