I use mink boxes, but there are plenty of better ways to catch mink. The trap I use for them is a 120 body gripper(conibear). It is the same size as a 110, except with 2 springs for extra killing power.
One of my favorite mink sets is a variation of the double dirt hole set that is used on land for fox/coyote. This requires a higher bank, at least 1-2 foot.
Punch one hole in the bank just high enough for a mink to stand on its tip toes to see in it, approx 2-3 inches wide. Punch in another hole 12-14 inches away from your first hole, 3-4 inches higher than the water's surface. Put a fish in one hole and a mink lure in the other. Both holes should be around 8-12 inches deep.
Put your trap in the middle of the two holes. The idea is that the mink will see both holes, and check both of them, and when he's going from the first one to the second one you will get him. Having one hole higher than the other one will make his feet shuffle aound your trap longer.
You can also put traps on either side of the holes in addition to the one in the middle, to get him if you missed him in the middle, or this is good if you have multiple mink in the area, and the middle trap already has a mink in it.
I have plenty of more sets for mink that I can share if you want me to.