The coax shielding should be grounded and will be if you mount the antenna properly.
You could have a bad radio, bad coax, bad antenna or bad ground.
Start with ground, make sure your antenna is mounted correctly per the link posted above.
Make sure your tire carrier is grounded to the body. Make sure the body ground straps are in good condition.
Next, make sure your swr meter is working properly, try it on another radio if you can or try a different swr meter.
Next, I would get a shorter piece of coax. As posted above, don't roll up any extra in loops.
Make sure you're getting about a third or more antenna above your roof line.
"But it does me no injury for my neighbour to say there are twenty gods, or no god. It neither picks my pocket nor breaks my leg." - Thomas Jefferson, Notes on the State of Virginia, 1782
Arguing with a truck driver is like wrestling with a pig in mud, eventually you realize the pig enjoys it.