Verb object
Who is the object of the verb in this sentence - "Was willst du mir sagen"? (What do you want me to say?)
Is it "you" or "me"? Is that even a correct sentence grammatically speaking?

Question

Verb object
Who is the object of the verb in this sentence - "Was willst du mir sagen"? (What do you want me to say?) 
                                                                                                          Is it "you" or "me"? Is that even a correct sentence grammatically speaking?

Answer

It's an interrogative sentence, not a declarative sentence, so let's look at the declarative sentence first:

Du willst mir etwas sagen.

du = subject
mir = dative object
etwas = accusative object

So the question "what is THE object" doesn't make sense, there are two objects.

In the interrogative sentence, you can exchange one of the objects for an interrogative pronoun:

Wem willst du etwas sagen? (Asks for the dative object)
Was willst du mir sagen? (Asks for the accusative object).

Don't try to understand German grammar by translating it; English only has one kind of of object.

Answer

To me, it seems as though "me" is the object and "you" are the subject, so shouldn't it be "mich" and not "mir"?