If the song seems to make no sense lyrically, that’s by design. Mick Jagger says the band utilized the “cut-up” technique popularized by William S. Burroughs to assemble the verses.
Here’s how he described the process to Uncut magazine in 2010:
That song was done in cut-ups. It’s in the style of William Burroughs, and so-on. ‘Million Dollar Sad’ doesn’t mean anything. We did it in LA in the studio. We just wrote phrases on bits of paper and cut them up. The Burroughs style. And then you throw them into a hat, pick them out and assemble them into verses. We did it for one number, but it worked. We probably did it ‘cos we couldn’t think of anything to write.
No good, can’t speak, wound up, no sleep
Sky diver inside her, slip rope, stunt flyer
Wounded lover, got no time on hand
One last cycle, thrill freak Uncle Sam
Pause for business, hope you’ll understand
Judge and jury walk out hand in hand
Dietrich movies, close up boogies, kissing cunt in Cannes
Grotesque music, million dollar sad
Got no tactics, got no time on hand
Left shoe shuffle, right shoe muffle, sinking in the sand
Fade out freedom, steaming heat on, watch that hat in black
Finger twitching, got no time on hand