The mink got inside my coop because I forgot to close the door one night, and my run wasn't predator-proof. Much hardware cloth has been added, along with double rows of 12-inch square concrete stepping stones along the outside edges of the runs.
I have learned it's not wise to speculate on this forum, but I, personally, would think it's unlikely that a mink would dig that much. I feel like they are much more opportunistic and look for an easier kill. Again, that's just my opinion. Someone else may be able to better answer that concern.
I don't know if the moles are your diggers. The tunnels I've had to contend with out here have been dug by rats. A few years ago, they constructed passages that led between two of my coops and would pop up in the runs to steal leftover feed.