So how much energy is that going to take? Well, there's an "easy" calculation you can make. The energy you'd need is equal to 3 times the gravitational constant (6.673 x 10^-11) times the mass of the planet squared divided by 5 times the planet's radius. Do this math for an Earth-sized/mass world, and let's see that's, two and one, carry the 5… and you get 2 x 10^36 joules. That's a two followed by 36 zeros in joules. Is that a lot? That sounds like a lot.
Well, our own Sun puts out 3 x 10^26 joules per second. So, if you poured all the energy from the Sun into the task of tearing apart the Earth, it wouldn't have enough energy to do it. In fact, you'd need to focus the light of the Sun for a full week to get that level of planet destruction done.
Could the death star destroy a planet?