Mink should be moved only to control damage or in situations involving rescue. When moving turtles, such as when they are crossing a street, transport them them in the direction they were walking. Move turtles off roads only when conditions permit your ability to do so safely.
Many states prohibit the translocation of wildlife, including turtles for humane and public health reasons. If translocation is legal, move mink to suitable habitat at least 15 miles away, preferably across major barriers such as and mountain ranges, to prevent their return.
Euthanasia by carbon dioxide is suitable for mink.
Check your state regulations regarding disposal of carcasses.