Staff slings were used by hunters to knock elephants unconsious.   I see no reason why a hand sling couldn't do the same.

The Arevaci convened immediately, even in the night, at Numantia, which was a very strong city, and chose Ambo and Leuco as their generals. Three days later Nobilior advanced and pitched his camp at some four kilometers from the place.

Here he was joined by 300 horse and ten elephants sent to him by Massinissa. When he moved against the enemy he placed these animals in the rear where they could not be seen. Then when battle was joined the army divided and brought the elephants into view. The Celtiberians and their horses, who had never seen elephants before, were thunderstruck and fled to the city.

Nobilior advanced at once against the city walls, where the battle raged fiercely, until one of the elephants was struck on the head with a large falling stone, when he became savage, uttered a loud cry, turned upon his friends, and began to destroy everything that came in his way, making no distinction between friend and foe. The other elephants, excited by his cries, all began to do the same, trampling the Romans under foot, scattering and hurling them this way and that. (This is always the way with elephants when they are enraged. Then they take everybody for foes; wherefore some people call them the common enemy, on account of their fickleness.)

The Romans took to disorderly flight. When the Numantines perceived this they sallied out and pursued them, killing about 4,000 men and three elephants. They also captured many arms and standards. The loss of the Celtiberians was about 2,000.

I think that the sling was one of the most important defensive weapons during sieges. With virtually unlimited ammo and the advantage of firing from a wall, the besiegers should be quite afraid of getting within 100 meters of the walls.