Ok so let's say my opponent has a Festering Mummy (It's a 1/1 and when it dies put a -1/-1/ counter on target creature) and I cast Splendid Agony (Distribute two -1/-1 counters among one or two target creatures) and I put a -1/-1 on the Festering Mummy, is it considered to have died and does its death effect still occur?
Festering Mummy's triggered ability will trigger.
"To die" is synonymous with "to move from the battlefield to the graveyard" (for any reason). This includes when State-Based Actions move a creature to the graveyard for having negative toughness.
Creatures that have 0 or less toughness will "Die" according to state-based actions.
This is covered by the following two rules:
704.5f: If a creature has toughness 0 or less, it’s put into its owner’s graveyard. Regeneration can’t replace this event.
700.4: The term dies means “is put into a graveyard from the battlefield.”
So for your specific example what will happen is:
- You cast Splendid Agony targeting your opponent's Festering Mummy.
- It resolves placing one -1/-1 counter on Festering Mummy.
- State-based actions see that Festering Mummy has 0 toughness, and moves it to the graveyard (i.e. Festering Mummy dies).
- Festering Mummy's death ability triggers and goes on the stack.