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 fire axe he sees himself giving Blu heavy a giant lollipop. And instead of setting things on fire with the flamethrower, he's growing flowers 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.