If Starman is heading to Mars, why is he still spinning so we see the earth? Shouldn't he always be pointing away from the earth?
Starman and its stylish choice of transportation are sitting atop the second stage:
The stage itself may be using spin stabilization, which helps by providing gyroscopic stability and thermal distribution. If you observe the live feed, you may notice that it is spinning in a counter-clockwise motion.
Once disconnected from the second stage, the payload may preserve the original momentum.