We had mink problems in a chicken barn many, many years ago on the Oregon coast. Mink are smarter than crappe, and can be quite vicious to people as well (don't ever attempt to grab one!). My mom finally killed a repeating offender with a long/heavy Brinkmann flashlight, finally catching him within an 8' x 8" coop, AFTER he/she had killed just about every bird in the coop. She was ******! (is this O.K. to say?)
I have never lived in an area with mink populations since, so I am certainly no expert on nabbing/killing the dastardly devils. I have dealt with other predators over many years though.
Would a double-ended Iive trap increase your chances to catching the wary-yet-smart vermin? Peruse these kinds of traps at Livetrap.com (no...I don't work for the company!), or another source of well-designed live traps. Throw out those worthless Havahearts? Been thar, done that.. I couldn't even catch the dumbest animal on earth (an armadillo) with ours.
With a "double-set trap" , you set BOTH ends of the trap to open, making it a bit easier to entice Mr. Wary into entering/passing through. If the animal has been trapped, and escaped from any type of live trap before,...this may not work at all. Animals are smart.
Bait the trap with something "fishy" like Fancy Feast near the treadle in the center of the trap, dropping a SMALL amount of "cool food" near both openings.
If ANY trap has been fouled by blood, or human scents, the mink may readily pick up on this. Prior to use, clean with an oxidant (like peroxide...then rinse), or an enzyme cleaner, to eliminate smells that you can't see,...but your mink may easily pick up on.
Good luck!