Stunning Strike is in addition any damage caused by the attack.
There's nothing in the wording of the effect that indicates that the other effects of the melee attack are changed by use of stunning strike:
When you hit another creature with a melee weapon attack, you can spend 1 ki point to attempt a stunning strike. The target must succeed on a Constitution saving throw or be stunned until the end of your next turn.
(PHB, p. 79, emphasis mine). Note the bolded text: stunning strike isn't itself a melee attack; it's an effect that can be applied when a melee attack hits.
Compare this to the language used to describe the Disarm combat option (DMG p. 271, emphasis mine):
The attacker makes an attack roll contested by the target's Strength (Athletics) check or Dexterity (Acrobatics) check. If the attacker wins the contest, the attack causes no damage or other ill effect, but the defender drops the item.
The rules for stunning strike don't have any such language to indicate that the attack's regular effects don't occur.