I am going to add a 12V LED strip of lights under my 310RL and going to tap into the "ground effects" LED light. See pic. Can I just cut/strip this wire?
That would not be a good idea.
It isn't best practice to splice into a circuit that is already suppling a load. In this case, I would trace that light circuit back to its feeder wire and make the connections at the larger feed wires.
You could use a terminal strip, or cap splice to attach the multiple branches to the feed.
If you spliced into that light, you now asking that lights very small gauge wire to carry more amperage.