Creutzfeldt-Jakob from squirrel brains
https://www.foxnews.com/health/man-dies-from-extremely-rare-disease-after-eating-squirrel-brains

Chronic Wasting Disease from deer, elk & moose
http://www.virology.ws/2015/03/11/is-chronic-wasting-disease-a-threat-to-humans/

Tularemia from rabbits and prairie dogs
https://www.cdc.gov/tularemia/transmission/index.html

Bovine TB in deer
https://www.cdc.gov/tularemia/transmission/index.html

Bird transmissible diseases
https://www.medicalnewstoday.com/releases/61646.php

and all of the tickborne diseases
https://www.cdc.gov/ticks/diseases/index.html

Please double glove with nitrile gloves while cleaning, and dont allow brains, spinal cord or spinal fluid to contaminate the meat.

Protect yourself, and your dog from ticks
http://nymag.com/strategist/article/effective-tick-repellents.html