Baumel was raised in New York and attended the Hebrew Institute of Boro Park before his family immigrated to Israel and settled in the Haifa suburb of Kiryat Motzkin. He went to the State Religious School as well as Midreshiat No'am High School.
After his studies, he began his military service in the Israel Defense Forces in the Hesder format which combined army service with religious studies. Baumel played basketball frequently and studied at Yeshivat Har Etzion in Alon Shvut. In the army he became a tank commander. Before the First Lebanon War, Baumel had nearly completed his military service and was preparing to study psychology at Hebrew University.
On June 11, 1982, in a battle with Palestinian and Syrian forces near the Lebanese village of Sultan Yaqub, five Israeli soldiers went missing. While two have since been returned to Israel, three others -Tzvi Feldman, Yehuda Katz and Baumel - are still considered missing in action.
Shortly before the fateful battle, Baumel had sent a postcard to his parents telling them, "don't worry, everything is okay, but it looks like I won't be home for a while."
In February 2011, the Born to Freedom foundation obtained a photo believe to be showing the body of Baumel atop a Syrian tank; nevertheless, he is still considered missing in action until further proof of his death arises.