How big of a hole do you need for a mink box and will a "Victor Professional Rat Trap" with the large yellow trigger, hold or kill a mink.

A two and 1/2 inch hole works fine for mink. "NO" on the rat trap!

That trap won't kill or hold a mink.

Here is another option for a mink box...

IMHO the best box set up for mink is a pan trigger trap recessed close to the bait into a 14 inch or longer box. Although mink are accustomed to tunneling through vegetation, it is my understanding and experience that, many will often balk at the cold, hard and stiff wires in their face at the box entrance and shy away from entering. Whereas with a pan trigger trap set CLOSE to a concealed bait at back of the box, and nothing in their face, they will proceed to enter and investigate further thus stepping on the pan and getting caught.