Always check with local electrical codes, but here is a brief description based on the NEC handbook.
To ground the dish to the structural ground, you can use either the wire attached to a messenger coax cable or run a separate 10 awg copper wire from the dish or mast and bond to the structural ground. A tapping screw would give good connection to the mast, but if you use a clamp, always the scrape paint to bare the metal for good electrical contact.
If the mast or pole is set in the ground, you should consider that it may also be providing a potentially dangerous exposure for a grounding potential. Ground mounted poles and grounding rods driven to provide a secondary grounding point are to be bonded to the structural ground by a minimum 8AWG wire.