Thankfully I've never been dismasted, but have always carried some form of cutting tool, should I need to deal with the problem.
I don't think most realize the urgency of cutting a mast away if it were to go over the side in foul weather, but it could be critical to one's survival to be able to do so quickly and efficiently. Imagine how easily a mast would go through the hull of your boat if the seas were up and it was smashing into the side repeatedly.
I doubt there there is a set of manual cutters that would quickly and easily cut 13mm 1X19 s/s wire, so we carry an electric grinder. I've cut 3/8" bbb chain in well under a minute, so I imagine the wire would go a lot quicker. I can wrap the motor in a plastic bag if things are wet on deck, so that's not a huge concern.
Let's hope none of us ever need to deal with this, but as mentioned above, an ounce of prevention is worth a dozen pounds of cure; check your rigging often! A month back we found an after lower on the main with 3 broken strands at the deck end and we check frequently, so it hadn't been that way long.