you're right, the wrong slimes have a puff of smoke and multiply, but killing the right slime could have some sort of indication on the remaining slimes that they are now vulnerable
The concept was "an arena shooter where only one enemy is killable", so you're hunting the specific slime that can be killed so that you can wipe the rest of the enemies
If you kill slimes at random, you'll just make the situation worse for yourself with more and more slimes swarming you :)