Familysearch.org indicates that an Arthur Mitchell (b. 1889)registered for the military draft (WWII) in 1942 and at that time he lived in Patterson, Passaic, New Jersey. Social security information at the site, indicates that an Arthur Mitchell died January, 1968 in Patterson, NJ. I am not sure if these individuals are the same, or the one you are looking for, but I hope the information is helpful to you. You may wish to view the information above online at the ancestry.com site for free at a local library.