half-shafting refers to a procedure done to stock throttle bodies. The stock throttle body has a shaft that holds the butterfly in place. The butterfly is a piece of metal that opens the throttle body (TB) up depending on how hard you are pressing the gas pedal. The shaft is cylindrial and the butterfly sits right in the middle. The idea of half-shafting comes from removing the front/top side of the shaft from the butterfly. This is supposed to increase the amount of air and lower the turbulance of the air entering into the upper intake manifold. aka - more hp. However, the stock TB's shaft isnt really that obstructive. Especially since the V6 mustang isn't exactly a powerhouse needing that extra <5cfm of air that half-shafting does. I would say it could be good for about 1/2bhp. not enough to justify it.
Aftermarket TBs generally come half-shafted. The makers just mount the butterfly to the back of the shaft and call it a day. It is beneficial in high horsepower cars because those shafts tend to be a little bigger, and aftermarket TBs just eliminate it and increase bore. The manufactuers just put the two together on all products made.
That being said, I have no idea what year car you have, but if you have a 60mm TB on your car already, I am thinking you have a 99-04 model. You have no need to goto a larger TB. The stock one actually flows enough. You really only need to goto a larger one if port the upper intake, or add a power adder (turbo or supercharger). Also, if you put that 60mm on your stock upper intake, you are actually losing hp. The stock intake is not meant for larger bore TBs and there is a small ridge where the TB meets the manifold. This is causing blockage and turbulance of the air going into the plenum. Not good. If you were to bolt a 70mm TB on, then you would NEED a power adder and a modified upper intake manifold. Don't do it.
Remember, just cause parts makers have parts for the mustang, doesn't mean it's a good part. They count on the unknowing to buy their parts and keep them in business. That's where knowledge comes in. Put the stock TB back on, sell the 60mm to some one else. Or at least port your own upper intake manifold