If Stabbing Pain targets an untapped creature with 1 toughness, that creature gets -1/-1, then it becomes tapped, then (after Stabbing Pain resolves) it’s put into the graveyard as a state-based action. Similarly, if Stabbing Pain targets an untapped creature with 1 less than lethal damage marked on it (such as a 3/3 creature with 2 damage marked on it), that creature gets -1/-1, then it becomes tapped, then (after Stabbing Pain resolves) it’s destroyed as a state-based action. In each case, any abilities that trigger when that creature becomes tapped will trigger.

You may target any creature with Stabbing Pain. It’s okay if it’s already tapped.