So your husband used WEED WACKER (as we say in America) on your potato plants.

Yes there is a chance that they might recovere if there are some stems left of them. Just manually clean up the chopped stuff, take care of them (water, fertilize). You should see some new growth. Just wait and see. But they might not be as productive.

Your husband is dumb. Pardon me for saying so.

I'm pretty sure they will recover since they have energy stored in the seed piece and roots. It's still fairly early in the season for you.

You must be down under, so I suspect the plants had already done a majority of their vegetative growth. I suggest dig a couple up and see if they have formed any new potatoes yet, if so harvest them all. Either way they are unlikely to make much more progress - the little sprout the old tuber will put out after having put nearly everything into the first attempt will not amount to much. Better off using the ground for something else unless you have loads of garden space.