The ability granted by Spiteful Sliver will trigger even if the Sliver is dealt lethal damage. For example, if a 2/2 Sliver blocks a 7/7 creature, the Sliver’s ability will trigger and it will deal 7 damage.

Damage dealt by the Sliver due to its triggered ability isn’t combat damage, even if it was combat damage that caused that ability to trigger.

If a Sliver is dealt damage by multiple sources at once (such as by two creatures blocking it), its ability triggers once and one target is dealt that much damage.