How far it needs to be moved would help. If yours is like mine the pipe is probably PVC for the main runs and then a flexible tubing for the last few feet. If you are moving a short distance you dig up the flexible and rotate it to the new location. If it is farther than that, then the difficulty increases because you will be stubbing off the pipe and digging a new trench.
I am needing to move the sprinkler head about 6'. My main question is do I have to shut off the water to the sprinkler head before moving cutting the PVC pipe?
No, the main valve for that particular watering station will keep water from flowing through the head; make sure that you run the line level so that the sprinkler head isn't too high, it's always easier to make a head higher than lower...
no, not as long as the pipe you are cutting is downstream of the valve that controls that zone. if you cut it at the place where the head is attached and simply extend it 6 ft, then you don't have to shut anything off, just make sure you controller is off.
I would suggest tho that after making the extension, you turn that zone on and run water through the extension before you put the head back on to insure all the dirt and debris is out, will save you frustration when it comes to unclogging filters.