One notorious pest of potato plants are cutworms. Unfortunately due to the the discoloration of the species I am not able to identify for sure which species of cutworm it is.
Cutworms attack a wide host of plants (more info here). According to that same website, the main ways to avoid the damage these larvae can cause are to:
Remove all plant residue from soil after harvest or at least two weeks before planting...
... plastic or foil collars fitted around plant stems to cover the bottom 3 inches above the soil line and extending a couple of inches into the soil can prevent larvae severing plants; hand-pick larvae after dark; spread diatomaceous earth around the base of the plants (this creates a sharp barrier that will cut the insects if they try and crawl over it); apply appropriate insecticides to infested areas of garden or field if not growing organically
These larvae come from a large variety of insects so don't associate them too quickly with one insect or another (many websites associate them with moths but that is not always necessarily accurate).
Here's a source that elaborates a bit more on how to treat them plus another source for how to use pesticides in a garden safely (if no other option is convenient).