Note that this card states that a Stardust monster needs to be "on the field" in order to activate this card. It doesn't say on which side of the field it needs to be on. Take advantage of that by using an opponent's "Stardust" monster to fulfill the requirement, allowing you to destroy a card on the field, even without a "Stardust" monster of your own.
Beware though; many "Stardust" monsters have effects which negate destruction effects ("Stardust Dragon" being the prime example) which can make this card counterproductive.
This card can be run in a "Duston" deck in order to support the archetype's boss monster: "Starduston.