It is a reference to the 'cycle/circle' of life. Cause and effect: What goes up must come down (another Lyric).
The real question is what does the "Ride a painted Pony, Let the spinning wheel ride"...
The spinning jenny was a multi-spindled machine. So is the spinning mule. :) (I found the information on this website. All I did was type spinning mule and spinning jenny :) )