system
Given the following post, respond as if you're commenting on Reddit:
human
[Star Wars] Ok, we have perfected spaceflight, some inter-dimensional travel (hyperspace), killed teddy bears and built lightsabers... Why the flip does nobody know what a radiator is?

So picture this:  You've got this ridiculously hot superlaser for destroying planets that irritate you.  You've got a powerful reactor core that generates ridiculous amounts of heat.  You vent heat out to space with... vacuum?

You don't need womprat-sized holes that lazurmonks can shoot proton torpedos at, you need a circulating liquid coolant system that passes through the frigid cold of space before zipping back to the core.  Rust?  Build it out of aluminum and use an OAT liquid.  Concerned about leaks?  Line it with durasteel.  Worried that someone will disable your pump?  Install 10,000 pumps, each with its own cooling lines, then monitor pressure and heat mitigation for each one continuously.  Price?  It's a freaking dreadnought planet destroyer, SPARE NO EXPENSE!  Worried that some @$$#01e space-monk will shoot your exposed grill and damage your cooling system?  It's better than letting the same @$$#01e space-monk shoot a proton torpedo directly into the reactor.
gpt
You underestimate the sheer size and engineering requirements to build a small planet with a hypermatter laser strong enough to vaporize a planet instantly. Typically you build several prototypes and tweak the design. This isn't possible with a Death Star - and the second one had solved the exhaust port issue in any case.

As to your suggestion... piping liquid into space is a bad idea.