Costello, if i may....it's most likely it is a racoon and possibly 2 or 3! If it was a mink or weasel it would just eat the head...usually, the brain has the highest and best tasting fat content, at least to a,weasel. This past spring/summer i lost 12 young pheasants that were in my outdoor brooders. They were covered with 1inch chicken wire. At first i thought it was a weasel but there was nothing left not even feathers. So i put 1/2 inch hardware cloth around the bottom 8" of the brooders....still lost birds. They were strong enough to pull it down far enough to reach in and get to my birds.After this, i set steel traps...first night caught 3 coons. Set them again, a week later and caught 2 more. I haven't had anymore predation. If you can set some steel traps so that your dog can't get caught you might have a chance of catching the rascals. Of course you also risk catching house cats and any other animal that walks into the traps. If you use the live trap, bait it with a can of cat food....coons can't resist it. Also, make a funnel to the trap...it will act as a channel to the trap.
Hope this helps....i know what it's like to lose birds and can't figure it out.
Get some Duke DP traps. The DP stands for Dog Proof and Duke is the company name. These traps are coon catchers.