MESA, Ariz.—Wil Cardon, an Arizona Republican who unsuccessfully ran against Jeff Flake for the U.S. Senate seat in 2012, died Saturday. He was 46.

Mr. Cardon’s wife, Nicole, said he killed himself. Mr. Cardon suffered from depression, a disease that he battled with “openness and honesty,” his family said.

Mr. Flake said on Twitter that Mr....