The mini pekka hits very hard (i think he hits just as hard as the full size P.E.K.K.A but has less health) but is easily distracted. You can take him out by distraction, skeletons or goblins are great for this, and play them towards the middle of the field to get him away from your towers.
I have noticed that a lot of players now use him with a hog for a very powerful rush, that only costs about 8 elixir. If the Mini P.E.K.K.A and the Hog reach your tower it goes down in about 3 seconds or less. So make sure you have the elixir to counter this move.
you can also distract him with a canon in the middle of the field, by the time he has walked over there and back to your tower the canon and both tower damage will have taken him out. Add some spear goblins or other small troop if you want him to go down even quicker.