Actually, Mirror Wall will typically be activated during the Damage Step, during which Twister can't touch it, and often so that one opponent's monster gets destroyed in the process. Destroying it afterward won't mean much when it already did its job, and because of its prohibitively high LP cost, it rarely lasts more than one turn anyway.
Twister can be activated when your opponent uses Mirror Wall and as per Wall's effect "each enemy monster that attacks has its atk halved as long as this is face-up" by using Twister you destroy the Wall, and since it's not faceup, your monster's atk pts goes back to normal.
Know your spell speeds
Twister is a quick spell, so in the chain, twister is considered to activate first (due to faster speed) and since mirror wall is a continuous trap, once it is popped, the effect does not go in to effect allowing the board to be mirror wall free
TLDR: Quick Spell Speed > Continuous Trap speed, so it is as if mirror wall never got used
The original post is talking about how Mirror Wall will most likely be activated during the damage step. Rules state; the only thing that can activate during the damage step is altering ATK/DEF cards and Counter Traps. Twister is a quick-play that destroys S/T cards. You won't be able to activate it during the damage step no matter the spell speed.
There is some glitch that you can activate twister against it in the damage step. I'm not sure how i was able to. I swung with my dino, he flipped to reveal wall, my dino's stats shrunk. Then I was given the option to use my twister?! I used it and my dino's stats returned to normal and killed his monster. It made no sense but somehow i was able to