Spectral Thief does damage. If successful, it also steals the target's stat boosts (if any) right before doing damage. Spectral Thief bypasses substitutes.
Spectral Thief will steal all stat boosts; even if the sum of the user's existing stat boosts and the target's stat boosts exceeds +6 in a stat, the target's stage will become 0. If the user has the Ability Simple, then the stolen stat boosts will be doubled; if the user has the Ability Contrary, then the stat boosts will be inverted.