Goodness! So sorry to hear about your sweet potato troubles. Here are some thoughts.
1) If you think it might be squirrels, you might visit the following page for tips on control: http://www.almanac.com/pest/squirrels
If you think there is a possibility that another animal, such as a rabbit, might be the culprit, here is an article that helps to identify what animal might be causing damage: http://www.almanac.com/blog/gardening-blog/be-critter-detective
http://www.almanac.com/pest/rabbits
2) You might dig up one potato to assess its condition. If it looks like it needs a little more time, then wait for the harvest a little longer. If the vines are still green, it could be that the potatoes are still getting the nutrients they need to grow/mature. If the vine is starting to yellow at the tips, or a frost is expected, then harvest them as they are.
3) Try to identify the exact culprit, whether it is entering the garden from holes underground or from climbing the fence. If from overhead, you might, as the least expensive option, try covering the plants with row covers or plastic tunnels. A determined squirrel may chew through it, but it might deter some. Chipmunks can easily get under those, however. For those the burrow, as well as climb, a more elaborate physical barrier system may be needed to enclose your garden (such as wire overhead fencing to deter climbers, and wire mesh buried in an L-shape pointed outward along the perimeter to deter diggers). Motion-detector sprayers might be another option. Repellents may also help.
Goodness! So sorry to hear about your sweet potato troubles. Here are some thoughts.
1) If you think it might be squirrels, you might visit the following page for tips on control: http://www.almanac.com/pest/squirrels
If you think there is a possibility that another animal, such as a rabbit, might be the culprit, here is an article that helps to identify what animal might be causing damage: http://www.almanac.com/blog/gardening-blog/be-critter-detective
http://www.almanac.com/pest/rabbits
2) You might dig up one potato to assess its condition. If it looks like it needs a little more time, then wait for the harvest a little longer. If the vines are still green, it could be that the potatoes are still getting the nutrients they need to grow/mature. If the vine is starting to yellow at the tips, or a frost is expected, then harvest them as they are.
3) Try to identify the exact culprit, whether it is entering the garden from holes underground or from climbing the fence. If from overhead, you might, as the least expensive option, try covering the plants with row covers or plastic tunnels. A determined squirrel may chew through it, but it might deter some. Chipmunks can easily get under those, however. For those the burrow, as well as climb, a more elaborate physical barrier system may be needed to enclose your garden (such as wire overhead fencing to deter climbers, and wire mesh buried in an L-shape pointed outward along the perimeter to deter diggers). Motion-detector sprayers might be another option. Repellents may also help.