I had the same problem. My advice is:

1. use a couple ninjas with mystery damaging entire team (Tenten, Kinkaku, Gaara, Kankuro etc.), they will help to sweep the field from Puppets.

2. You can try to use someone like Kakashi Beheading Sword, his mystery skill won't allow Sasori to be resurrected.

3.Don't forget about good combos.

I used water main:

Kinkaku - x - Sakura GNW

x - x - x

Kankuro GNW - x - Water main (2-2-4-3-2 talents) with Ninja monkey or Deer as summon