¿Que quieres que diga?

¿Que quieres que diga? Why not ¿Que quieres me diga? What do you want me to say?

I think the second question would be "What do you want me to say to me?" Isn't "diga" 1st person subjunctive? I believe that literally the first statement is "What do you want that I say?" The "me" in your second statement becomes the object that is receiving what is being said. Therefore the question becomes, "What do you want I say to me?" I very well could be wrong, but that's what it appears to be at first glance to my mediocrely trained eye. ;)

Diga, I think, can be 1st person subjunctive as hefay says, but also 3rd person/singular subjunctive or 3rd person/singular imperative, no? Aurora, is "what do you want me to say?" the translation given for this question?

Yes, "diga" can be 3rd person singular also, but I think the imperative is "di." So perhaps ¿Qué quieres que diga? has two meanings. What do you want me to say? What do you want to say? So then using "me" would change it to: What do you want me to say to me? What do you want to say to me? I'm not sure, about any of this, just thinking out loud. I'm absolutely sure that I am not a quotable expert.

The English translation is what do you want me to say?

Hola a todos, I agree with The Hefay. It is the subjunctive and the literal translation is, "What do you want that I say?" and the English translation is, " What do want me to say?" I try to internalize things in Spanish and not get hung up on the literal translation, but that's just my approach. Saludos, Ricardo

Diana said that "Que quieres" is "What do you want?"."Que diga" cannot exist by itself but 'Que quieres que diga" is "What do you want me to say?" Another translator said "Que quieres decir" is "What do you want me to say" but Diana said that "Que quires decir" means "What do you want to say?" or "What do you mean by that?". Sorry about the absence of the accent of the e in Que.

I also looked ahead at the future lessons and I found that the subjunctive mood is going to be discussed in Level 3-Platinum Level Lesson 15. I decided to just be patient and continue with the lessons until I reach the Platinum level where subjunctives are.

Good call. There are times in language learning where you just have to set certain subtleties aside and hit them when you're better positioned to tackle them in the future.