You can only save the game once you get your wig pushed back or kill a boss, if you die you start from the beginning, if you kill a boss you can skip to where you killed the boss although you may be at a disadvantage since you don’t keep your gear.
So the way these games work is you work your way toward a boss, you most likely will die, and you lose all your shyt. You progress further because you just learn how to play better like an old school arcade game.
The catch is that you get a couple of things that you get to keep each time you die, like gun proficiency and ether you can spend on different upgrades
If you quit the game inbetween a restart and a boss it will be automatically counted as a death.