Many states have restrictions on relocation of foxes, so check with your state wildlife agency before relocating a fox. Due to the risk of rabies, foxes should only be relocated in rescue situations.
Many states prohibit the translocation of foxes because they are a common carrier of rabies. If legal, foxes should be moved to suitable habitat at least 20 miles away from the capture site, preferably across major barriers such as rivers and mountain ranges.
Euthanasia by carbon dioxide is suitable for foxes. When performed properly, shooting the animal in the back of the skull is appropriate.
Check your state regulations regarding disposal of carcasses.