From a pure physics point of view, there must be energy stored in the knife that, when released, does the work of pushing the blade out. Obviously, that energy is stored in a spring. This is not unlike most any automatic knife. The question is, how do you get the energy in?
If you've used one of Microtech (or other) conventional OTF autos, for example, you know that to close the knife, you pull out on a mechanism usually called a "recharge lever" (though it's not a lever in the physics sense). When you pull out and then push back that mechanism, you're doing work. Part of that work is to pull the blade back in. Part of it is to compress spring, to store energy, which will later be used to move the blade forward again.
With a DA auto, you do work when you move some mechanism, typically when you pull back on a sliding button. Some of that energy pulls the blade back and some of it is stored in a spring. Obviously, no mechanism can be 100% efficient. When you use one of these knives, you'll notice that pulling back on that slide is actually pretty hard. I've seen people with weaker hands, some women, elderly, etc., unable to get that slide to pull back with just one their thumb.