Oh, so I guess the old fashioned way of rubbing it down a bit with a little birdie’s beak every 1000 years is not going to work for you?
Using the worst possible collection of half assed numbers, I think we would need to move the entire volume of the top 10 largest open pit mines in the world 23 times over.
You don’t take it from the top down and you don’t remove it from the bottom up and you don’t drop bombs on it. You drill and shoot controlled explosions to create multiple huge networks of terraces and ramps.
You would likely use very long conveyor belts, uses far fewer trucks and roads, and additionally you dont need a road up the outside -
Build access to the higher levels with tunnels - so no worry about the weather, which is the main cause of death on Everest. The tunnels can go to the outside eventually but it would be easier to cut away most of the rock from the inside. It would also enable 24 hour working.
I would take 100 years and 6 trillion dollars.
I was going to say, this sounds like a problem for XKCD’s What If?
The MOAB would be really effective against people, but I don’t think it’s great for blasting away rock. It’s an air burst weapon, so most of the energy from the bomb would just be dissipated in displacing air. If you wanted to blast away the mountain, you’d probably have to use bunker busters of some sort.
I tend to think the directional drill/explosives method that sitchensis mentioned would be the way to go, setting off a series of landslides. Assuming we just need to level it down to base camp, we’d have to move ~60 billion m3 of material… so a couple thousand Frank Slides or so.
Well, we can argue over whether the OP is a bad idea 
but the OP specifies doing this with Western Health and Safety standards.
I don’t think it’s possible to trigger that kind of collapse for any remotely reasonable definition of safety.
Think about how the process goes. You start carting away the base. Small collapses occur. The remaining mountain gets higher, steeper, and more unstable. bigger collapses occur. At some point you have a really high really big really unstable mountain and it falls way the hell over. How big a boom does it make? How do you get the people who are hauling rock away out in time?
The idea of using drones to deliver explosives to the top may be the most workable solution.
If we just blow up the mountain, or reduce it to rubble - don’t we just have a pile of (smaller) rocks basically the same size as when we started?
So that people won’t notice until it’s too late.
I say train yetis with backpacks. They can see in the dark, right? That’s why no one ever sees them. Start with maybe 20, each taking down, say 100 pounds per week (because they can climb faster than people). As they get used to the process, add more yeti. Maybe get a bucket brigade line going.
How long will it take? I think I’ll let the yetis do the math. They’re good at math.
Redirect a large enough or enough smaller NEO space rocks to vaporize it from above. Would solve the earth warming side of climate change as a side benefit.
Build several nuclear reactors to power a giant fricken laser beam.
We could use the rubble to fill that huge godawful canyon out west. Put that real estate to use.
And the rest of this is such a good idea?
Tris
I propose waiting for natural erosion to do the job.
Wouldn’t erosion do the job before then?
This seems beyond the ability of the common super rich person. Also the laser could maybe vaporize the rock which would recondense and rain out, so just making it a pile of rock drops.
Sadly, the “What If?” column has been moribund for almost 2 years. I guess there just isn’t the big money anymore in the “Ask the web genius.” business.
I’m willing to put my stamp on “very slightly less terrible”.
Maybe? Depends on what the Indian and Eurasian tectonic plates do?
No need to show my math because you could never understand it, but the answer is: 42.
I am afraid you got it all wrong, the best, probably the only way to solve this problem is to paint Everest pink and use a Somebody Else’s Problem-field as shown by Douglas Adams with precisely the same example: taking away a mountain.
Just convince Vladimir Putin that Everest is valuable and he’ll steal it.
Not only that – we start by taking rock downhill – it’s self powering.