Every time I've wanted to replace windows, I've only had to boot to an installation disc (as yancek has already discussed) and allowed the install process to reformat and repartition the heard drive.
Boom. No more windows. I'm not sure where you got the idea that a 'puter running windows was somehow protected from being overwritten.
In fact, I once was trying to build a dual-boot on my Dell laptop and answered a question the wrong way...no more windows. Oops!
Back in the day, one had to give partitioning instructions during the install. Of late, I believe the installations have a default partitioning setup they'll use.
At some point in the installation, you should get a message to the effect that "This will destroy all data on the drive!!" Answer yes to that and you'll have no more windows.
Edit: some of yancek's excellent instruction was to help you with dual-booting windows and mint. I'm reading your OP that you don't want to dual-boot, so some of what they said doesn't apply if that's the case.