Both of ours are just yard dogs although both probably would have made excellent hunters if they had a bit more time and education as pups.
A male jack Russell terrier and a female lab, they actually make a good team hunting in the yard. The JRT never stops and the lab does all the heavy work. Have watched her lift sheets of iron so the JRT can get to rats and mice he has cornered.
Their best effort was a fox in the yard, they woke me at about 1am with the JRT going more ballistic than normal, wouldn't come to the back door so I investigated with a torch. One fox cornered between the bird aviary and fence, when the JRT finally flushed him out the lab really surprised me, I expected her to grab it by the throat/neck and shake but she simple grabbed it by the chest bit and crushed until it stopped moving and then released it. She is a very large dog close to 100lb and I've watched her dispatch rabbits and rats the same way. Despite this she is very soft in the mouth when she chooses, she will pick ripe tomatos and drop them at the back door without marking them.