Why does the outlet short out when I turn on the garbage disposal?
The receptacle that the disposal is plugged into is fed from the Load side of the GFCI receptacle, thereby providing ground fault protection to the receptacle. There is a ground fault somewhere between the GFCI and the disposal, which is causing the GFCI to do it's job and trip.

You'll have to locate the fault, and fix it. If you don't have (or know how to use) a multimeter, you'll want to contact an Electrician.  If you have a multimeter and know how to use it, you can narrow down where the fault is by checking continuity between hot and ground.

Start by turning off the breaker, and insuring power is off in the area you'll be working. Unplug the disposal and do a continuity test between the hot blade (smaller blade) on the plug, and the ground pin (long roundish pin).  If the test shows there is not fault in the disposal, move up the circuit to the next device (receptacle) and test again (don't plug the disposal back in). If you still haven't found the fault, continue working your way up the circuit (the switch next) until you reach the GFCI. If you still haven't found the fault, try replacing the GFCI receptacle (making sure to hook it back up the same way).

If you still cannot resolve the issue, it's probably best to call in an Electrician (since they'll have cooler gadgets to troubleshoot the circuit). I would focus most of my attention on the disposal and the switch, since those tend to be the usual culprits.