Just wondering... are you cutting wire into small pieces? I've seen people do it this way and it just seems easier for me to don leather gloves, roll it up and only cut when the roll gets too heavy. I hang the rolls on a fence post and then go back and pick them up with the truck or tractor. I've rolled up lots of decrepit wire and it usually stays together.
we use heavy duty wire-cutting tools from Lowes, works great. Helps that hubby has strong hands.
Hands are not made for brute strength tasks.
When it is hard, find a better way.
Smaller bolt cutters will preserve your hands, if you have much wire to cut.
For a bit of wire here and there, be my guest, use whatever you can manhandle to work.
the key is to be super organized about picking up the wire as you cut it. With brush growing up through the fence, you'll end up having to cut irregular lengths. Believe me, you can cut a piece and it's right at your feet and you think let me cut that other one and pick them up together--and just like that, that 1st piece has disappeared in the grass and you'll be desperately scrounging around for it.
And wear safety glasses!!!! Wire is so unpredictable, you really have to respect it.
If you are doing electrical work on the upstairs renovation then you might want to invest in a pair of electrician's pliers or linesmens: they really work for cutting wire, plus they have plier tips for getting at the barb wire that has grown into the trees.
This will sound weird, but I am reading this thread and daydreaming about the day I cut down the nasty old barbwire at my new place. It is negative windchill out right now and we are supposed to get six inches of snow in the next few days...