OK, but how long will that beam stay in contact with the same spot?
I still don't see this thing slicing through a whole missle making two distinct parts that will then fall harmlessly to the ground. At best I see a bunch of holes that might hit the missle's equivalent of a CNS, but moreso maybe not.
So the stoopid guy still needs this 'splained to him.
stay safe.
As others mentioned, just melting a single spot on a missile in flight will usually destabilize it almost instantly.
However, the targeting issues with the laser to keep it on one spot on the missile to really damage it have been solved for some time now too. The Airforce ABL mounted to a 747 can do it in theory, and has even solved the atmospheric distortion issues with adaptive optic mirrors. They're flexible, and have dozens (thousands?) of little actuators that ripple the mirror to exactly counteract the ripple in the atmosphere, as driven from the input of a lower powered test laser.
http://www.youtube.com/watch?v=mCufvG9TE8wAstronomy has been using this tech to get near-Hubble quality issues from the ground for a decade or more now.
http://www.youtube.com/watch?v=cxelYpoYpzAAnd the THEL system, a chemical laser housed in a couple of conex-type shipping containers, with a steerable head the size of a spotlight has shot down Kayatusha rockets in Israel.
http://www.youtube.com/watch?v=LThD0FMvTFUThe new Tactical Battlefield Laser fired from a C130 can pick out a spot on a pickup trucks hood and burn through it and disable the engine while orbiting in a circle at several thousand AGL.
http://www.youtube.com/watch?v=UaMQNgqT1iUThe technologies of targeting lasers and beam shaping are getting pretty mature.
The issue is getting away from the expensive, complex, and difficult chemical powered lasers that run various (and often corrosive/toxic) chemicals through what is essentially like a jet engine or wind tunnel to produce the beam.
There's also great advancements in diode and crystal based solid-state lasers, but they have upper limits on their power output because they still require physical media to lase. They're way easier to deal with than chemical lasers, but eventually you reach the limits of the lasing media, and the solution is to just stack more and more of them together, which gets bulky, and requires ever more complex optics to get all the disparate beams together into one.
The FEL just wiggles electrons past a series of magnets kind of like the teeth in a zipper, yanking the electrons back and forth so violently, they emit synchrotron radiation as photons, and modulating the "wiggle" by timing the electro magnets, you can tune the laser. So there's no gases or chemicals that need to be handled, and no crystals or diodes that will fry when you turn the power up past what they can handle. You can leave it running 24/7, the only limitation is the input power.
So as others mentioned, put a nuke reactor in for power, which means a ship, and you can see why the Navy's got a boner for this.