Dr. Joseph Glazier was born in Indianapolis and has been a resident of Indiana all his life. At the age of four, Joseph was involved in an accident that resulted in a broken arm. The emergency room doctor that treated him did so in a compassionate and kind manner. Immediately following this event, it occurred to Joseph that he wanted to pursue a career in medicine.

Due to Dr. Glazier's academic background and high grade point average, Joseph was accepted to Butler University who permitted him to take part in the accelerated pre-medicine program. There, he received a double major in zoology and chemistry upon graduating in 1970, cum laude. He continued his medical education at Indiana University Medical School, where he graduated in 1973.

In 1974, he began his Family Practice internship at Memorial Hospital of South Bend. According to Dr. Glazier, this important program enabled him "to obtain a general background in multiple medical disciplines". The following year, he began his Anesthesia residency until its completion in 1977.