My mother's house recently sold, but the new owner said I could go dig up some plants (if the snow ever melts!). She had a lovely red hibiscus that is several years old and I was wondering if it is possible to shovel prune a piece off. Any ideas would be appreciated.

You could, or you could cut a few, healthy 12" canes off, and stick in ground, two thirds, they'll sprout.
Either way, they won't bloom this year.

what type if ' Hibiscus " are you talking about ?....

Rose of Sharon ,, or the perennial kind that freezes back each winter ?

for rose of Sharon ,, you can take cuttings.. root them in 2" of water, then plant out later in the summer

Herbaceous perennial hibiscus can be propagated by dividing clumps in early spring.
Lift the clump out of the soil with a shovel. Use your fingers to work apart the large clump into separate smaller clumps, each with a healthy root mass to support the stems.

Perennial herbaceous hibiscus.

Thanks for the information!

Being N.Y. it must be The Database

We have quite a few listed in our database https://garden.org/plants/sear... and looking at information on a few, it does say they can be propagated by stem cuttings as well as division. As @mikelzz stated you can divide the clump being sure to get a few with roots attached for transplanting to their new location.