Not On Your Tintype Meaning

(idiomatic) An answer indicating outright rejection or denial; no way; absolutely not.

Example:   He got out an enlistment blank, and placing his finger on a blank line said, "Sign here." I answered, "Not on your tintype." "I beg your pardon?" Then I explained to him that I would not sign it without first reading it. — Arthur Guy Empey, "Over the top", 1917