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I've been having this idea about hit points and thresholds that I'd like to share with you guys. I'm sure someone already came up with the idea but if it did, I missed the thread.

So Hit Points are an abstract notion that includes luck, parries, blocks, evades, fatigue, mental stamina, etc...

With this definition of hit points, why doesn't a bull rush or a sleep spell deal damage? You're using your blocks, evades or experience to avoid the bull rush. You're fighting off the effect of sleep. Having these actions deal damage makes sense with that definition of hit points. The only problem is that you don't want everything to be "just damage" and you want the effect of sleep or bull rush to go off before the monster hits 0 HP.

My idea is to combine these "effect damage" with damage thresholds. Spells such as sleep, or bull rushes, trips, and so on all deal damage. Whenever you are the target of such an attack, you decide whether to defend yourself or not (before the attack and damage roll). If you decide to defend yourself, your opponent rolls an attack and damage roll as normal. If the damage exceeds your threshold, you are affected by the "special effect" part of the attack. If you don't defend yourself, you are automatically affected by the attack but take no hit point damage.

I'll give an example. Lets assume that you have a physical defense that represents your ability to avoid physical attacks (trip, bull rush), and a magical defense that represents your ability to avoid magical attacks (sleep, slay living).

Special attacks would look like this:

Sleep
You deal 3d6 effect damage (Wisdom half). If the spell deals more than your target's magical defense rating, the target falls asleep for 1 minute. Damage exceeding your magical defense is ignored.

Bull Rush
You  deal 4d6 effect damage (Strength half). If the attack deals more than your target's physical defense rating, you push the target 5'. If you beat your target's physical defense rating by 5 or more, you push the target 10' instead. Damage exceeding your physical defense is ignored.

Hamstring
Make a regular weapon attack roll. If the attack deals more than your target's physical defense rating, the target's speed is reduced by 10' for 1 minute. If you beat your target's physical defense rating by 5 or more, the target is also knocked prone. If you beat your target's physical defense rating by 15 or more, you chop his leg off.

These are the benefits I see to the system:

1. All classes use the same mechanics to take down their enemies. It's not on the one side spellcasters that blast their enemies with save or die effects and melee that hack into hit points. Everybody is dealing hit point damage, and when you're a little lucky, you get added effects.
2. Save or die/save or suck are less potent against tougher opponents without having to tweak the success rate. Sleep can always have a 65% chance of success against all critters. Weaker opponents would fall asleep automatically, stronger opponents would require both a failed save and a high damage roll to be affected.
3. The scaling mechanism is easy to implement. Thresholds increase with level and so does damage. A sleep spell in a 5th level spell slot might deal 7d6 damage instead of 3d6 damage. Monsters of the same level as the PCs would have defenses that increase accordingly.
4. Non-damaging melee options such as Bull Rush and Trip always are a valid option because they also deal damage.
5. Shields could increase your physical threshold. I think the game would be more interesting if the choice between a 2-handed weapon and a sword and board wasn't just chosing between +1 to AC and +1 to damage.
6. You can bring back mechanics such as spell resistance or spells such as antimagic field or globe of invulnerability. All of these could be modelized as damage reduction against spells.

Anyways, what are your thoughts? Too complicated? Too abstract?

First of all: in your system, do people still have hp totals? Because it sounds like you could ditch those.
I think your idea has potential but not that much of it. Here are my main issues with it:
1- It sounds incredibly very much NOT like D&D.
2- It sounds too complicated, specially in the D&D enviroment. 
3- It is, in fact, too counter intuitive. Having sleep deal damage is weird.
4- It is also very abstract, so it doesn't really solve most of the abstraction problems of hp (at least that's how I see it)

Still "if it deals more than X damage, do Y" sounds like an interesting idea. 

I really like the idea of Sleep as a method of taking your enemy alive.  In any case, it's also exactly the sort of thing you would want to use in a hostage situation.

Not dealing damage is a benefit of some spells and abilities.

It's taking the abstraction to another level. Like reasoning with metaphors; money is speach, corporations are people, ergo the federal and state laws cannot abridge a corporations ability to spend money.
 Effects end after a designated period. Damage lingers until healed. Healing shouldn't counteract the sleep spell. Yelling and shaking a bleeding body should not increase the amount of usable blood in the body nor seal the wounds.

i dont understand why Hamstring doesnt do damage using your reasoning?