Destroying a planet doesn't break any laws of physics, it's just that as seen in the movie, the Death Star does not conform to any currently known requirements on how to do that. It would need enough mass to provide the energy required (well over 2.4E32j in the case of Earth). The Death Star would more likely look like two giant spheres joined together, with the sphere in tow encasing the enormous small moon sized amounts of mass required for the needed energy. Issues such as getting rid of excess heat, or just plain exploding, are challenges to overcome.
A laser could make a planet explode even though it only targets a specific area. A laser with enough energy (it would be better to use Gamma rays) could pierce through the planet, heating it up as it does so. The entire planet would melt and then vaporize (You would need ENORMOUS amounts of power to do this in a reasonable time frame). The next stage is continued high-power heating to create a plasma in which the velocities of the particles exceed the gravitational binding energy of the object as a whole. This would mean that outside of influence from other bodies, all the particles exceed their local escape velocity, making the planet permanently destroyed. You'd better not be in the way when this happens though.
This would be ridiculously inefficient and uneconomical. I know the Death Star is a terror weapon, but it's not worth its cost in resources. It's much more practical to bombard the surface of a planet and turn it into an uninhabitable wasteland. The worst part about the Death Star is that even when it fails after only one demonstration, the Emperor orders a new, EVEN BIGGER one to be constructed WITH THE SAME WEAKNESS AS BEFORE. Gah. This would be like if Nazi Germany squandered all their money on creating a 100 meter long super cannon, it was destroyed after only one shot by a guy shooting a pistol into its heat vent, and then they went and wasted all their money building an EVEN BIGGER 1km intercontinental death cannon WITH THE SAME WEAKNESS AS BEFORE...
The most nonsensical part of the Death Star isn't the physics; it's the logistics.