It would still take a huge amount of energy to overcome the gravitational force between the two halves.
If you want two moons, your only choice is to blow the moon up into bits and pieces. Then work on getting those pieces to coalesce into two moons.
A more worthwhile effort would be to build a huge observatory and base smack in the middle of the far side. You'd get about 6 weeks of unobscured viewing. You'd relay data back to earth via satellite in lunar polar orbit.
I think the Chinese will do this (the observatory and base).
The moon only weighs a sixth as much on the moon as it does on Earth.
And each half weighs half a moon, or one twelfth as much as on Earth.
You could pretty much pry them apart with your bare hands.
Where would you find a saw blade long enough to go through all that Cheese?