Both options are possible in the conversational speech in some known dialects of English.
Though, in the modern written speech the sentence *You have done everything you can do* is  rare and historical.
*You have done everything you could do* is more widely used, but, it needs a clause or phrase denoting purpose of the action. For example, *You have done everything you could do to fulfil the task*.Without such clause, the sentence *You have done everything you could do* is semantically somewhat incorrect.