Jomo, to avoid the armful backlash from the vice-grip, you get a giant backlash from your strong springs and heavy hammer head. The pet nails cutter pushes you in a way which doesn't seem right to me. The rope and many other things like a simple paper sheet or some meat are very hard to cut just by pushing a blade straight on them. The fibers fold on the cutting edge, making a cushion around it, stopping the blade's progression. The force to overcome that is enormous compared to the cutting force itself.
Put a sliding movement on the blade, and suddenly the cut becomes easy.
For example, you have obviously the rope and the handsaw, but too the trimmer in the printing industry. This one is a heavy duty press with a massive razor blade, but it could do almost nothing on a big pile of paper if it didn't manage a small lateral movement of the blade along its length. Look at your knife when you eat a steak (and I don't mean a Macdo's) ( but yes, even a Macdo's for that matter).
I know that the cutting thing is your baby, so I'd keep that as a given.
Something you could look at is the cutter blade for the carpet, it has a hook shape (centering the rope in the curved edge, so no reject of the rope nor the blade), the right size for a small rope or fishing line and easy (I think) to find. Give it a lengthwise movement with a slight angle through the rope. No need of a heavy mass to move, just ensure some travel, don't know how much, maybe 2". That shouldn't be bad.
It looks like that:
Or something like a film cutter:
Otherwise, you have the guillotine style:
but with a partially open area to slide in sideway the rope.
You get the idea...