Save points are those small white boxes with smiling faces on them that save your current position when you shoot them. Upon being shot, they will frown, turn pink, their eyes will turn red, exclaim "Fuck you!", and spit a blue ball at the player. Since shooting them saves your game, getting hit by its projectile will not hinder your progress. The amount of save points throughout the game varies with the difficulty level.
In the boss rush room, there is a save point with a red R on it. Like a standard save point, it saves your game and briefly turns hostile, but in addition, it resets the timer and death count, and turns green boss thumbnails back to red, reviving defeated bosses.