The sheer physical energy of the laser will rapidly turn matter into plasma (certain efficiency and coupling effects will be enhanced or degraded depending on the wavelength of the beam, but I suspect that at these energy levels the amount of difference it will make will be overshadowed by the scale and scope of the beam itself).
In the first microsecond, the atmosphere under the beam will immediately be turned into a superheated ionized plasma, expanding rapidly outwards from the strike. The idea anyone within a few hundred kilometres will survive being lashed by supersonic waves of plasma is questionable, at best.
Striking the surface will result in substantially the same thing, rock, soil, plants etc will be converted into a star hot plasma. Interestingly, the plasma will try to "run up the beam". but the extreme heat and electrostatic repulsion of the ionized plasma will tend to drive it apart, resulting in a massive inverted cone of plasma leaping out of the ground and into the vacuum the beam has created. For areas outside the immediate strike zone, a supersonic shockwave will blasting away from the area, continuing to excavate a larger and shallower crater entered on the strike zone. Something very similar will happen if the beam lands in the ocean or body of water, the main difference being the plasma will be largely hydrogen and oxygen, rather than an unholy mess of silicates, metals and organics.
Burrowing through the crust will take a bit of time, although the massive pressures developed by the plasma will clear out the laser channel and prevent the hole from collapsing due to static pressure. The oceans might actually allow the planet to survive for a time, since water will continually try to flow into the plasma "hole" and the boiling sea water will carry a great deal of energy into the atmosphere, meaning the beam might have to dwell for a while to evaporate enough ocean to strike the seabed.
Assuming you haven't targeted the edge of a crustal plate or the magma chamber of a super volcano, the beam will continue to the point where static pressure is finally able to overcome the pressure of the expanding plasma. You will already be feeling earthquakes, but now the beam is "pushing" on inflowing rock (at the scale of planets, matter should be treated as a liquid). Depending on the depth of the hole, magma or even plastic rock from the mantle might be flowing into the hole to be immediately vapourized. An observer in orbit will see the huge inverted cone of star hot plasma exiting the atmosphere and accelerating into space. Some of this may "condense" around the edges of the cone, and shower down around the planet, igniting a global firestorm. Much of the remaining atmosphere may well already be poisoned by various oxides as the hot plasma reacts with atmospheric oxygen.
If at this point the laser is stopped, there will be a sudden inflow of rock, water and gasses into the huge vacuum that was created by the laser and expanding clouds of plasma, generating more violent storms, earthquakes and tsunamis. The surface of the planet will have been scoured by supersonic waves of plasma streaming outwards from the strike zone, and as the plasma cools, the surface may well be covered with a thin glassy layer of rock vapour that condenses on the cooler surfaces.
If the laser continues for a prolonged period of time (I don't have the math to figure this out, but intuition tells me this will take several hours), the pressure waves of the plasma will be moving through the mantle and around the core, creating violent earthquakes on the opposite side of the planet. As an aside, the planet will also be getting some severe earthquakes due to the plasma plume acting as a rocket engine and pushing against the Earth as well.
In terms of planetary destruction, the laser will fairly rapidly strip off the planetary atmosphere, by heating the gasses to well beyond the escape energy required to leave the gravity well. The water will be eliminated by a similar process, but lasting for a considerable period of time, given the massive amounts of water on the Earth. Carving a hole in the crust will trigger violent earthquakes, but shattering the crust or lifting massive chunks of the Earth bodily into space is likely not going to happen for a while yet. The increasing amounts of energy in the mantle will stir the plastic rocks there violently, triggering massive earthquakes and probably shattering continental plates along the edges, but until the mass of rock reaches the point where it is essentially turning into "steam", you won't see the crust blow off into space.
Once the crust is blasting into space because the mantle is turned into vapour, we should consider the core. The violent pressures in the mantle will actually increase the pressure on the core, but asymmetrically. As the amount of matter over the core is suddenly reduced, the core will violently be disrupted, and the huge amount of energy from the heat and pressure will be dumped into the remaining mantle, "splashing" it violently into space.
So I do hope someone can do the math to get some real times, but my sense of the matter is the laser will strip life off the surface in a short period of time, but will need more than a day to impart enough energy throughout the mass of the planet to actually blow it up.
