I use a Dremel tool to cut cables for a perfect finish. The basic tool is not much different in price to a pair of decent cutters, and you can also use it for other tasks (if you’re so inclined). I’m not convinced that your problem is coming from this, though. If the outer was crushed, you’d get slow/stiff shifting through the range, not just a jam at one end or the other. Probably.
Have you checked the derailleur hanger? I have a spare (new) hanger in my trail bag and it’s also been out a couple of times to check if shifting problems are coming from the one on the bike being out of shape. If you can’t swap yours out, you’ll really have to get a shop to put an alignment tool on it as a problematic bend can be impossible to see visually.
With the cable disconnected completely, can you manually shift the chain from one end of the cassette to the other?