the Best Way to destroy the Pyramid is graphically depicted in the last panel of “The Hardest Head in the World” by renowned MAD artist Don Martin.
It’s in his book Don Martin Bounces Back (the same one that has National Gorilla Suit Day), but I can’t find an image to post here.
A couple of privates and a butterbar and tell em to clean it.
The problem is that your proposal as phrased is, in terms of orbital mechanics, gibberish. 
First, you can’t shoot something past the sun in order to accelerate it in the sense that you mean. Don’t get me wrong, the sun accelerates things constantly, and moving something closer to the sun will increase the acceleration it derives from the sun, but that acceleration is mostly acceleration in terms of altering the direction of travel and not in terms of making something go faster or slower relative to the earth. You can’t use the sun’s gravity well to do any kind of gravitational slingshot in the way you’re thinking - the sun’s gravity can’t alter your orbit around the sun, because that’s what your orbit is. You need another gravity source that’s moving relative to the sun.
Second, the delta-V requirements to fire something close to the sun are ridiculous. You basically have to cancel out most of the earth’s 30km/s orbital velocity. Then all you’d get is a highly eccentric orbit, and assuming you calculated correctly and that your projectile arrives back in the vicinity of earth, the encounter would be best described as the earth running into the projectile rather than vice versa. In this case you’d be better off expending the ridiculous amounts of fuel you burned by accelerating straight at your target.
Third, if you really want something to be moving at very high speeds relative to earth you’ll be best off using Jupiter’s gravity well to set your projectile onto a highly eccentric orbit that crosses earth’s orbital path at roughly right angles, which should get you into that same 30km/s range while having only expended a tiny fraction of the energy.
Really, you’d know all this if you played Kerbal Space Program. 
Yeesh, all you need are a couple thousand big red rock eaters.
Also, .9999 planes on treadmills will take off exactly the same as 1 plane on a treadmill.
The point of the sun was to turn the craft around, not make it go faster.
And it’s a better choice than Jupiter because of the symbolism, which is why we Don’t let nerds make these decisions.
I can’t believe you resurrected that beast! We could use the mass from that thread alone as a kinetic weapon to take down the pyramids!
Except…by resurrecting it, you might have caused a black hole to form on the earth, dooming us all!!!
Michael Bay covered this in one of his documentaries. The Constructicons combine for form Devastator, which is able to shred that puppy to reveal the Sun Harvester.
The sun won’t turn the craft around in the sense required by your plan.
They’re built at the same angle as sand and gravel collapse into. They can’t collapse no more.
The best way for one to be blown up would be if it went in the air, flipped over and landed on its tip exactly where it is now.
Just ignite the grain dust.
They were built to store grain, right?
No miners here? Just drill blast holes in a 10m x 10m grid through the whole thing, pump in ANFO, stand back a safe (very safe) distance and boom! Sorry, the thing won’t disappear. It will just collapse on all sides into a pile or broken limestone.
Is there a time limit? Can we wait for climate change and aim a glacier at them?
There’s an old saying in the Marine Corps: Lock two Marine Privates in a windowless concrete bunker, with nothing but an anvil in it. Open the door an hour later, and you’ll find the anvil broken and both Privates missing.
I’ve heard the Army has a similar saying as well.
So on that note…
A full battalion of Army and Marine Privates and PFCs - over a thousand of them. Bus/truck them to the pyramids, tell them not to touch the pyramids, then leave them there, with no adult supervision. Come back in a few hours to a few dozen Privates throwing fist-sized chunks of pyramid rubble at each other because they’re bored.
Or tell them there’s a log of chew and a carton of reds SOMEWHERE in there.
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That’s what happened to the limestone casing, but it took centuries.
The cocktails and strip joints aren’t as good either. Weather’s about the same.
Well, Hell.
Devise a plan whereby the Earth is crashed into the Sun. That’ll fix them.
Cutting off your nose to spite your face?
You see how well that worked with the sphinx.