Squirming Mass

Let's say the Mass is 1 power, and it fights another 1 power minion. What happens?

Both take 1 damage each, which results in their simultaneous death. That triggers Squirming Mass's ability, which means its gains +1 power, but it's already dying, and merely gaining power isn't enough to save it. (Something specifically that saves a unit from death would be necessary, like Gilded Aegis.) In this example, both minions are placed in the cemetery.

If a minion's current power is different from its printed power when it dies, which value does Squirming Mass gain?

The current power of the minion that dies.