There is an entire tourism section on the government site for the dam. On the matter of the spillways, it says (emphasis mine):
Watch the spillway in action between the months of December and February when the steel floodgates are open during the rainy season. The opening of the spillway does not follow a preset schedule. It is directly linked to the level of the lake. Those lucky enough to watch the water draining out through the three chutes have the chance of beholding an unforgettable display. The outflow of Itaipu's spillway is equivalent to 40 Iguazu Falls. That deluge slides down a 30 meter toboggan to form a 10 meter overflow, and then finally goes back to the rocky bed of the Paraná River, at 40 meters deep.
The dam as a whole sounds pretty cool, even without that, but I would say if you're visiting in the rainy season you could perhaps try to go when it's been raining a lot?