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