Easiest way would be to pull the cut harness out of the dash & take it to a junk yard. Hope that you can find an exact replacement. Second would be to track-down a factory wiring manual & splice into the damaged harness. I've seen wiring manuals on e-bay. Neither is what I would call an easy project.
This "database" has wiring color codes for various vehicles. Here's the one for the 2012 F150. If your vehicle is a different year, it's probably different.
Depending on the age and condition of the vehicle (and the extent of damage to the factory wiring), it's sometimes easier to just run new wires. Then you only need to identify and locate 2 wires, "constant" and "switched" power, unless your vehicle has a power antenna or if you really have to have the "illumination" to function properly. "Ground" is any bare metallic surface. Running new wires to speakers usually isn't much of a chore.
Get some wire strippers and some 18 awg butt connectors. Match the new harness color by color. Then, connect the other end of the harness into your stereo.
YOU CAN BUY THE HARNESS NEW FOR YOUR TRUCK IF YOU ARE PUTTING AN ATERMARKET (NEW)RADIO 2 OPTIONS BUY THE NEW HARNESS OR DO WHAT IVE DONE MANY TIMES SPOIL OF SPEAKER WIRE AND RUN YOU VERY OWN PLUS THEIR THICKER MORE CONSTANT POWER FLOW=BETTER SOUND AND ALWAYS SHOOT FOR A 1 OHM AMP FOR BIG BOOMS.