Given that the goal was for no more cats to be born (so that the cat population eventually drops to 0) and this was apparently accomplished, it seems like a fair term.
"Driving into extinction" is an awfully loaded and hyperbolic phrase for "neutering a single colony of feral domestic cats." It makes it sound like an atrocity. Maybe that's not what you intended.
Preventing unwanted and uncared-for kittens is a good thing. It's a major goal of animal welfare groups all over the world.
