Use a very light touch with a heat gun to soften the adhesive. Then peel back the vinyl and clean up any residual adhesive with a polar solvent like rubbing alcohol. Non-polar (petroleum-derived) solvents can cause some substrates to cloud over, so don't use them. Even if this is not readily apparent, this can change their optical properties which won't show up until the sign is lit up, probably on the pole after it's already installed.
Do NOT use paint thinner or mineral spirits like toluene, xylene, naphtha, or varsol - these are non-polar solvents. On an existing sign you never know what material they used underneath. Polar solvents are generally water-based and won't damage the substrate but will still soften the adhesive enough to clean it off. Even Goof Off, which is very popular in the US to remove adhesive, can cause clouding in some polymers.
If the substrate is so badly abraded that it needs to be wet sanded or buffed, it's not worth the labor to salvage it. Recycle it and replace. My supplier will cut 51x100 sheets of acrylic to any size I want, since I can't fit that size sheet in my van (I just have to buy the whole sheet and pay for cuts)
Good luck.
Greg