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 only steal enough boosts to reach +6 stages in each stat; if the sum of the user's existing stat boosts and the target's stat boosts exceeds +6 in a stat, the target will retain any excess boosts. 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.