While attending Hokkaidō Urahoro High School, Azuma participated in the Hokkaidō branch office of COM, along with other artists such as Monkey Punch and Fumiko Okada. In 1968, after graduating from high school, he moved to Tokyo and found employment with Toppan Printing. He left this job after three months to work as an assistant to manga artist Rentarō Itai, where he did uncredited work for Weekly Shōnen Sunday on series such as Mini Mini Manga.
Azuma made his professional debut in 1969 in Manga Ō with his work Ringside Crazy. The following year he quit working as an assistant and doing his own work. He gradually expanded his work to include both shōjo and seinen manga. His first works tended to be light gag manga, though he began to include science fiction elements influenced by his being a fan of the New Hollywood movement in Americanfilm. It was during this period that he experimented a lot with one panel manga (as opposed to four panel).
Beginning in 1972, Azuma began rising in popularity due to the off-color humor in his Weekly Shōnen Champion series Futari to 5-nin. He also married his assistant the same year, with whom he had a girl in 1980 and a boy in 1983. His wife was credited as "Assistant A" in his works, and his daughter and son were respectively credited as "Assistant B" and "Assistant C".
Azuma began serializing in 1975 his story Yakekuso Tenshi in the semimonthly manga magazine Play Comic. He also began publishing science fiction themed works in many different niche magazines such as Kisō Tengai and Peke. Azuma, together with Jun Ishikawa, is considered part of the manga creators in the 1970s. Due to works such as science fiction novel parody Fujōri Nikki, published in Bessatsu Kisō Tengai in 1978, Azuma began to gain a large following among science fiction fans. Fujōri Nikki was awarded the 1979 Seiun Award for Best Comic of the Year.
From there, he began publishing in magazines such as Shōjo Alice, becoming a fixture in the pornographic lolicon manga business and becoming very involved in otaku culture.
In late 1980s and into the 1990s, due to stress from his hectic and demanding schedule during 20 years (to that point) as a manga artist, Azuma began drinking heavily, disappeared twice for several months to over a year, attempted suicide at least once, and was finally forcibly committed to an alcohol rehabilitation program. He published in 2005 a manga journal of this experience titled Disappearance Diary. In addition to being published in Japan, this book has been licensed and published in English, French, Spanish, German, Italian, Russian and Polish.