My questioin is pretty much in the title, Why do I keep reading in actionscript 3.0 that its a good idea to seperate the \'mind\' from the \'object\' when writing code?
If you're asking why graphics are separated from the positioning, movement and physics; take this tree I've drawn:

In the tree you'll see that Entity has two properties:
Moving down, you will see that there are several things that extend Entity - most notable are the Player and the Enemy classes.
Extending my Entity class above, I can easily change what should be used as the graphics and also provide slightly different bodies. For example, the player and enemies will have obviously different appearances, and the Tree class won't need to use a Body that deals with values like velocity because it doesn't move.
Here are some advantages of the above:
MovieClip if you had extended MovieClip with your Entity class.Graphics class such as being able to easily covert a Sprite or MovieClip into a sprite sheet for better performance.Body can be updated without immediate effects on the graphics.