Дайте is imperative. Also, 2nd person plural ("you guys"). Дай would be the singular form.
Чашку is Accusative. We are giving what? the cup (Accusative) to whom? to someone (Dative). Someone receives the result of the action (they would be in Dative, they are not in this sentence), and the action is done to the cup (it's the object of the action, it's Accusative).