Wither does not attack mobs
In the PC Edition, the Wither will attack mobs in addition to the player. They are supposed to attack every single mob that is not considered a 'dead' mob. (Such as Zombies, Husks, Skeletons...) In the PE, the Wither does not attack any mobs.
STEPS TO REPRODUCE:
1. In Creative or Survival Mode, spawn a Wither while there are also qualifying mobs closeby.
2. Notice it will entirely ignore them.