So I was on YouTube and saw the 'Meet The Pyro' video and I think I know the reason why he wears the mask; it's to hide every thing that he's really doing.
Like instead of him seeing that he's killing the Blu heavy with a 불, 화재 axe he sees himself giving Blu heavy a giant lollipop. And instead of setting things on 불, 화재 with the flamethrower, he's growing 꽃 and other stuff.
And also to keep him concentrated, so he doesn't wonder off and do other things. So to make a long story short the pyro needs the mask in order to kill other wise he would get to distracted.