Dana,  this is definitely not rabbit or deer damage.  It looks to me like slugs are at work here.  They feed at night, so they're hard to see.  I use Sluggo in my garden, which uses iron phosphate to control slugs and doesn't harm plants or insects.  It is OMRI listed for organic gardening. Organic Materials Review Institute reviews products to ensure they comply with all organic standards under the USDA’s National Organic Program (NOP).

Here is more information on slugs and how to control them:
https://www.extension.iastate.edu/news/2006/jun/070201.htm

https://hgic.clemson.edu/factsheet/snails-slugs-in-the-home-garden/

Thanks for contacting Ask Extension.