When powered by a Redstone signal, Karos Cannons will shoot a Vethean arrow out of one side. These arrows actually come out of the cannons, but Redstone equipment is normally unobtainable in Vethea, so in normal gameplay, this function is unused.
When Dream Flint is used to spawn Dr. Karos, the Karos Cannons will (supposedly) start shooting arrows across the room. However, the arrows aren't actually coming from the Karos Cannons, since when Dr. Karos is spawned outside the Karos Madhouse (in another dimension), arrows will appear from midair and travel just like they would if coming from the Karos Cannons, even without Karos Cannons to begin with. It is unknown if spawning Dr. Karos actually triggers the Karos Cannons. This is similar to the Heliotic Beam, which supposedly fires Karos' explosives in a similar fashion.
When right-clicked, the Karos Cannon will display the Dispenser GUI. This is probably a bug, since inserting normal Arrows still causes it to launch the Vethean arrows. This bug and the feature involving Redstone may be caused by Karos Cannons being derived from Dispensers.
Karos Cannons are stone-based blocks, and as such, are not harvestable in Vethea through normal gameplay. If you get a pick in Vethea through another mod, though, you can mine and keep the Karos Cannons.