Cordle told The Capital-Gazette that he would let his record speak for itself, but otherwise offered no comment. Neuman's spokeswoman Walinda West confirmed that Cordle was no longer employed with the county as of Friday.
Neuman and Cordle both vied for the executive's seat earlier this year after former executive John R. Leopold resigned.
Before serving as chief of staff, Cordle made an unsuccessful bid for Annapolis mayor in 2009 and previously had served nine years as an Annapolis alderman. In addition, Cordle served three commands in the U.S. Army. He lives in Annapolis with his wife, Michelle.