Well, a lot of this depends on just how advanced these beings are, and how much they can mess around with physics. The necessary answers seem to be "Utterly godlike" and "Physics? Why would we bother with that?"
The first thing to understand us that the Earth isn't a rigid, solid body, on the scale of the whole planet. It's a stiff fluid, some parts being runnier than others. The continents are made of less dense rock that floats on top of the denser rock. Think of it as a ball of very hot jello, with a thin and weak skin.
So if you just put a cut through the planet, nothing much happens, on the scale of the planet. It's held together by gravity anyway. There will be earthquakes and volcanic eruptions on a vast scale, but the planet won't come apart. It's possible there'll be some surviving life, but I wouldn't bet on it.
If you can put two planes of force through the planet and move them apart, then things get very exciting. The halves of the planet want to get closer together, but your planes of force prevent this, so they start to flatten out against the plane of force. The earthquakes and volcanic eruptions this causes should finish off all life, convert the oceans to steam, and so on.
If you carry on regardless then as the two halves get further apart they will start to reshape into spheres under their own gravity, and at this point "earthquakes and volcanoes" becomes utterly inadequate to describe what happens, and you end up with two balls of molten rock, with atmospheres about as hot as that of Venus. All this has been done by Earth's own gravity, plus the energy that was used to move the planes of force apart against that gravity. A lot of the heat in the interior of the planet has had a chance to move around, and has had fun.
If you want to make this survivable, it gets a lot harder, and you need aliens sufficiently advanced to utterly ignore the laws of physics. At that point, they peel Earth's crust off, including the oceans, not spilling anything, and only using very low accelerations so that mountain ranges don't collapse. You move the peelings out of the way, supplying them with artificial gravity so the atmosphere doesn't take off, and putting walls round them so that the oceans don't spill off into space.
Then you chop up the mass of the planet into however many chunks you want, separate them, let them become spherical, wait a few thousand years for them to cool down a bit (stopping time for the peelings) then re-surface them with selected pieces of the peelings, adjusting the curvature to fit. You will also need to fit these new planets with some means of artificially maintaining their orbits, or to redesign the solar system, but either of those problems is trivial compared to the peeling and resurfacing problem.
It would probably be much easier to just scan the entire planet and duplicate the geography, life and ecology by construction from scratch in another solar system that had the right size of planets naturally.
Off-hand, I can't think of an SF civilisation that could do this readily. The Culture could probably manage it if they did some development work. The Transcendent Powers of A Fire Upon the Deep wouldn't bother - what would be the point of it for them? Indeed, this is the basic problem: anyone who could do it is so far beyond human-scale interests that it's hard to write a story about them. Bob Shaw's The Ragged Astronauts has something a bit similar, set in a universe where the laws of physics are utterly different. Charlie Stross' Missile Gap has a peeled Earth, done by creatures whose motives are explicitly incomprehensible to humanity.