How do I remove the old plastic dishwasher water supply line connection near the shut off valve?
There are many ways to skin this cat. But probably the easiest one would be to cut the plastic pipe so that there is no water in it. The reason you want to remove the water is so that you can then use a hair dryer to get the plastic warm and soft. Use two pliers- one to brace the copper valve and the other to twist the plastic pipe or connector off. 

If that's not working, a pipe sander or dremel tool (with a cut off wheel) could probably chew through that connector pretty quickly, but I suppose you could also try using a box cutter to cut into the connector (which looks like it will be easy if it's warm and soft). But just be careful to not cut too deeply or you might damage some copper or brass threads. You should cut most of the way through the connector and then maybe use a small flat head screw driver to pry the connector loose.