There was no actual "single mix" for "Thrown Down"... that was just the phrase some fans used to distinguish it from the album version.
It's also been called the "Wall of Sound" version.

As gldstwmn pointed out earlier in the thread, it's actually an outtake from the 'Trouble In Shangri-La' sessions.

Ah right, cool. I didn't think it had been release as a single, but I wasn't sure. So were Lindsey's vocals just added then? What about drums and bass? If it's an out-take from one of her solo albums would John and Mick have been on it?

The majority of Stevie's vocals are the same as the album version, but the second line of the second verse ("here is a place that will never be dark -- I remember that place") is either from a different take or was re-recorded.

Hmmm. Now I have to listen to that again.

John and Mick aren't on that version, but Lindsey definitely is.

In 2000, Sheryl Crow talked to Billboard magazine and discussed working on 'TISL' with Stevie, and she mentioned that Lindsey had just been in the studio with them to record parts for two songs -- one of which would "really satisfy the diehard fans." (I paraphrased.)

(For the record, "Thrown Down" was released as a single in late November of 2003 -- simultaneously with "Steal Your Heart Away." But as they were released just as most AC stations were switching over to their Christmas music formats, neither received very much airplay.)

I've never come across a lossless version of that version of Thrown Down. I think it originally showed up on a German CD that was shipped to radio stations? Does anyone else remember that?
I like all versions of Thrown Down. I think the one in question would have sounded out of place on Say You Will though. The vocal and big rock sound are more compatible with Trouble In Shangri La, although it didn't quite with that record either.

There are some drum parts that definitely sound like Mick to me on that song. I'd like to know who did play the drums on it.

Yep thats part of what i was talkin bout. =)