If it is cut at an angle from two to six inches up, I would blame a rabbit. If they are munched from the top down, groundhog or deer.

But you are saying it is under the surface... If they are fairly flimsy from inadequate inside light and recently planted out, it could be slugs (especially if you have mulch down. If they are more dense stems, possibly cutworms. Perhaps earwigs. One way to find out would be to root around the soil about one inch, being sure to search plant litter up to two feet away, and see if you see any pests. Google for deterrents/traps, as there are a lot of suggestions out there.

A good preventative would be Sluggo Plus, that fights both earwigs and slugs. I always sprinkle Sluggo around my dahlias when planted out, until they are well-established. Don't know if the product works for cutworms, as I've never had a problem with them before.

No worries, the plant will grow back from the underground tubers.

One option is to take that two foot plant that is laying on the ground and stick it in a pot with soil, covering with a gallon ziplock bag or bread bag in the shade for a while. Keep it really well watered, until it roots in two weeks or so. Plant out after roots are well-established.