If a +1/+1 counter is removed after a creature takes damage, does it die?
Few points that should add up to an answer.

A Counter is not the same thing as a Static Ability that raises Power/Toughness.  Abilities that add counters will use the actual word Counter in them.  

Once a counter is placed, killing the creature that placed it does not do anything.  So if you have an Adaptive Snapjaw that evolved and is now 7/3 due to a +1/+1 counter on it, that counter does not go away just because the other creature that caused it to evolve dies.

On the other hand if you have an Elvish Archdruid making all your elves +1/+1, that is a static ability.  All your elves get smaller immediately when he dies.  Sometimes new players do get in the habit of putting physical markers on other elves to track such an ability.  This is a bad habit, I would recommend against doing it.

Damage does not reduce toughness.  The xBox game does it wrong, pretend you never saw it.  A 3/3 with 2 damage marked is just that, a 3/3 with two damage.  It is no way shape or form a 3/1 for any purpose.  So if your 3/3 with 2 damage marked is an Elf, and your elvish arch druid dies, he will become a 2/2 with 2 damage marked, and promptly go to the graveyard as well.