This Kryptonite gains superior cutting when energized by an outside power source. The Kryptonite glows brightly under the following instances:
- As a scalpel in the USAMRIID footage.
- As a scalpel wielded by Lex harvesting from Zod.
- As a spearhead drawn from the ground by Batman.
- As a spearhead under the rubble under the water.
The Kryptonite does not glow or glow brightly under other circumstances, including but not limited to the fragment in the box being shown to the senators, the spearhead plunged into the ground, the spearhead when forged, etc.
Something unifies the above tool uses. In every case, the Kryptonite is connected to a complicated scifi handle. Scalpel handles are simple and don't have triggers or cables coming off them, but they did in the above examples. Batman trained Robin to use a pole-weapon which is relatively straight-forwards, smooth and featureless, meaning they prefer standard simple shafts. Yet the shaft of the Kryptonite spear is incredibly complicated and technological, covered in flanges, flares, fins, rivets, ridges, rings, and reliefs… like a lightsaber… a weapon hilt which we know does more than simply act as a handle. This idea reinforced by Zack Snyder tweeting out an image of Henry Cavill clutching the spear-shaft with a red lightsaber blade emanating from it.
Additionally, when Batman draws the spear from the ground, it expands in two stages with a satisfying "Ka-chink!" sounds, indicating it has user-operated buttons or functions which allow Batman to expand the spear. If there are buttons or triggers to do that, then it's quite reasonable that there are buttons or triggers to power-on the spear. Just like there is a trigger for the kryptonite scalpel. If there is a button or trigger, then there is something for the rubble to hit or set-off when the spear is discarded off, but recovered on.
Why would kryptonite be better at cutting with energy in it? There's various precedent in real-world science, whether in ionizing a radioactive material or sending a cauterizing laser through a diamond crystal blade.
For more on the nature of Kryptonite in Batman v. Superman, Episode 44 of the MOSAIC podcast is all about the Kryptonite spear.