Be one the first ten mice to get to the shaman's cheese, as after ten mice touch the shaman, the shaman dies.
The golden name text on a selected mouse is listed as the Shaman-thief for the map. Keep in mind, though, that maps such as this one, where the thief steals the cheese, will not reset your points and you are very likely to be a normal shaman soon after. Avoid the mice. Because you both supply cheese and are a shaman, it is very easy and sometimes fun to troll other mice.
An easy method to get saves is to build a Bridge and then let the mice reach you.
If you would rather troll them, a basic solution would be to Wall Jump the side of the wall next to you. This makes many mice fall down the wall, due to finding it too hard to Wall-Jump with cheese.