Joseph (Joe) P. Haggerty was the first of three children born to Lt (USAF) Joseph H. Haggerty and Janice E. Haggerty nee Keller at Keesler AFB, Biloxi, Mississippi. Growing up in an Air Force family for 17 years until his father retired as a Lieutenant Colonel in 1973 after 22 years of active-duty service, he was exposed to the aerospace industry at an early age and was an avid fan of the space program beginning in 1961 with the flight of Alan Sheppard in Freedom 7. During his father's career, in addition to being stationed at various stateside bases, he also travelled with his family to Alice Springs, Australia, Clark AB, Phillippines, and Bangkok, Thailand where he graduated from the International School of Bangkok.

Originally planning to attend the U.S. Air Force Academy in 1973 to get a degree in Aeronautical Engineering and become a pilot, he found that he had partial color blindness and was therefore ineligible to fly as a pilot. Instead, he attended Florida State University receiving a B.S. in Biology in 1977. After a brief two-year employment in the Lee County Health Department, he attended the University of Tennessee receiving a Master of Public Health degree in 1979. He also met his future wife, Shauna, they married in December 1979, and together raised four daughters.

Still feeling the urge to serve his country, in 1988, after ten years in various healthcare roles, he applied for a direct commission to the Air Force, and in January 1989, was commissioned as a Captain in the Medical Service Corps. He also, like his father before, served in various military clinics and hospitals, including three years in tactical aeromedical evacuation. This resulted in his deployments to Germany, Somalia, Saudi Arabia, Haiti, and Thailand. Ultimately, he also retired from active duty as a Lieutenant Colonel after serving 22 years.