I guess it depends really, on the thickness and the type of wire. If it is multiple strands of wire then you will likely encounter the same problem as you did with the cable. Fibrous metal resists cutting quite well.
I have seen some barbed wire that is fairly thin and likely would be cut with ease by the Spirit. I have also seen some heavy duty stuff (I worked in jails for three years) that can only be cut by the jaws of life.
But, better to have the tools with you to try out than to not have the tool and never know!