I use a heavier fork than the standard pitch-fork/hay-fork. It is just what I have and I bought it to move mulch from truck/trailer to garden wheelbarrow. All my sweet potatoes are growing in 4'x4' up to 6'x6' boxes that rest atop the soil in my raised garden. These boxes were made to keep my various varieties of garlic separated. When I dig up my sweet potatoes it will be time to plant my garlic.
All my sweet potato plants are still lush with leaves. Generally by mid to late October, after a light frost or two, the plants will yellow, indicating it is time to dig them up. I start by digging down with the fork at the perimeter of the box, carefully turning that soil over, collecting any potatoes, and then moving a foot or so towards the center of the boxed in area. I don't bruise or pierce many potatoes doing it this way.
Rabbits here love to munch on the sweet potato leaves but the greatest munchers are deer. I have to cover all my leaves with a heavy plastic mesh to keep those critters at bay.