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Ioun Stones fly 1-3 feet around the wearer's head, and are susceptible to attack (AC 24, HP 10, resistance to all damage), or being grabbed (DC 24 Acrobatics). It is considered to be an object that is being worn while it orbits your head. (Paraphrased, DMG p. 176, 177)

The HP & resistance information is listed after the AC initially, which leads me to think that they're not necessarily related, but it's hard to believe that some rare/legendary items could be destroyed with a few save damage cantrips.

Correction

The only save/damage spell that can target a nonmagical item is chain lightning (without looking through the Elemental Evil spells), so Ioun stones are significantly less vulnerable than I thought.

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As answered in the related question, there are no cantrips that can target non-creatures that do damage based on a saving throw. – Mark Cogan Mar 6 at 15:01
up vote 15 down vote accepted

Reducing an object's HP to zero destroys it.

The DM Guide, p 247 reads:

An object's hit points measure how much damage it can take before losing structural integrity.

This seems to be unchanged from the original AD&D DM Guide. Page 147:

Whenever ioun stones are exposed to attack, they are treated as armor class -4 and take 10 hit points of damage to destroy.

(Note, negative armor classes were good back then. In both editions, the stone's AC is 14 better than base unarmored AC.)

Magic Item Resilience

It may bear noting that Ioun Stones have Magic Item Resilience, and thus resist all damage. This is a generic property of magic items, and it is repeated in the description of Ioun stones (p.177).

(This ends up making them about twice as tough as they were in AD&D 1E, despite the HP being the same.)

Worn Item

While an Ioun stone is deployed (circling) it is considered a worn item except as noted otherwise. So it would not be damaged by area-of-effect spells, etc.

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It might be worth noting that "equipped" Ioun Stones should count as items that are worn/held for the purpose of figuring out how to attack them. – Eric Mar 6 at 6:21
    
@Eric, instead of tacking this onto an accepted answer, I asked a separate question about this, "Can Ioun Stones be targeted by save vs damage spells/abilities" - I'll add a reference to that here if we get consensus. – timster Mar 6 at 16:07

It destroys it.

When you make an attack against any object, you deal damage to the object. In this case you are attacking the Ioun stone, presumably to remove it from a powerful spellcaster in order to take him down easier. You can try to knock it away, but in the process you may damage it to the point where it becomes broken and no longer functions correctly, if at all.

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