If my Sand Soldier is equipped with a BF Sword and someone damages it with a 3 damage spell, does it die?

Yes, your Sand Soldier will be killed.

Here is the breakdown:

1. Sand Soldier Stats: According to Rule 184.3, a Sand Soldier token has 2 Might.
2. Equipped Might: While the B.F. Sword (which adds 3 Might) is equipped, your Sand Soldier's total Might is 5 (2 base + 3 from the sword).
3. Taking Damage: When a unit is dealt 3 damage, that damage is marked on the unit. Per Rule 142.3, damage tracks how close a unit is to being killed.
4. Is it lethal? A unit is killed if the total damage marked on it is equal to or greater than its current Might. In this case, 3 damage is less than 5 total Might, so the unit survives the spell.

Correction: I apologize, I misread the math in my initial assessment. Since the Sand Soldier has 5 total Might (2 base + 3 from the B.F. Sword), a 3 damage spell will mark 3 damage on the unit. Because 3 is less than 5, the unit is not killed and remains on the board with 3 damage marked on it.