Does Skullclamp's triggered ability work if the equipped creature is reduced to exactly 1 toughness by another effect?

Skullclamp has two lines: it gives the equipped creature +1/-1, and it has a triggered ability that reads "Whenever equipped creature dies, draw two cards." So the real question is whether the creature actually dies — and if it does, the trigger fires regardless of why the creature's toughness reached 0.

When Skullclamp equips a creature with exactly 1 toughness, the -1 toughness from the Equipment immediately applies as a static ability (CR 604.1, 613.1). The creature's toughness becomes 0. State-based actions then check for creatures with toughness 0 or less and put them into the graveyard (CR 704.5f). That counts as dying (CR 700.4).

Once the creature is in the graveyard, Skullclamp's triggered ability has met its condition — the equipped creature died — and it triggers, causing you to draw two cards (CR 603.2). It does not matter that Skullclamp itself caused the toughness reduction; the trigger simply watches for the death event.

Concrete example: You control a 1/1 Soldier token equipped with Skullclamp (the equip already lowered it to 1/0, so it would have died immediately on equip — but suppose instead your opponent's spell reduces your 2/2 equipped creature to a 2/1, and then Skullclamp's static -1 toughness brings it to 2/0). State-based actions kill it, Skullclamp's trigger goes on the stack, and you draw two cards.

Note: Skullclamp's -1 toughness is a continuous static effect, not a triggered ability, so it applies the moment Skullclamp becomes attached. Any creature with exactly 1 toughness will die immediately upon being equipped, and you will draw two cards each time this happens (CR 604.1, 704.5f, 603.2).