Heyo. After block user (ban) he still has the same group. It would be nice to select specific group in Actions Settings and auto move users. What do you think? 

ACP -> Members -> Warnings -> Actions

Depends on how IPS looks as Banned.  If it is a status, then a group would not be appropriate.  Not much different than the way XenForo handles it.  What you can do there is run a "promotion" so that if they had a banned status, it would add them to a banned group.  With the limitation of promotions in IPS, that's not possible.  That would be a nice feature.