Spitzer was born in Timișoara in Romania. After his father died in 1956 when he was 11, Andre and his mother moved to Israel. He served in the Israeli Air Force and attended Israel's National Sport Academy, where he studied fencing. In 1968, he was sent to the Netherlands for further instruction in fencing for further training in The Hague with fencing master Abraham. Most of his first year in the Netherlands he stayed with the Smitsloo family in Scheveningen. In 1971, he married one of his students, Ankie. Andre returned to Israel with his wife soon afterward, where at age 27, he became the country's top fencing instructor. He helped found the National Fencing Academy, and became chief fencing instructor at the Wingate Institute.
The couple's daughter Anouk was born a few months before the Olympic Games.
The Spitzers went to Munich with the rest of the Israeli team, but young Anouk was left in the Netherlands, in the care of her grandparents.
Ankie Spitzer recalled her husband's idealism and attitude towards the Olympics:
(While strolling in the Olympic Village)... he spotted members of the Lebanese team, and told (me) he was going to go and say hello to them... I said to him, "Are you out of your mind? They're from Lebanon!" Israel was in a state of war with Lebanon at the time. "Ankie," Andre said calmly, "that's exactly what the Olympics are all about. Here I can go to them, I can talk to them, I can ask them how they are. That's exactly what the Olympics are all about." So he went... towards this Lebanese team, and... he asked them "How were your results? I'm from Israel and how did it go?" And to my amazement, I saw that the (Lebanese) responded and they shook hands with him and they talked to him and they asked him about his results. I'll never forget, when he turned around and came back towards me with this huge smile on his face. "You see!" said Andre excitedly. "This is what I was dreaming about. I knew it was going to happen!" (Reeve 2001, pp. 52-53)
Midway through the Olympics, the Spitzers were summoned to the Netherlands - their daughter had been hospitalized with an incessant bout of crying. After they arrived, they were told by the doctors that everything was fine and that Andre could rejoin his teammates at the Olympics. Andre missed his train, but his wife drove him at breakneck speed to the station in Eindhoven, where he boarded the train without a ticket.
Spitzer arrived in Munich about 4 hours before Palestinian members of Black September broke into the Israeli quarters, killed coach Moshe Weinberg and weightlifter Yossef Romano, and took Spitzer and 8 of his teammates hostage.
Spitzer was seen once during the hostage crisis, standing at a window in a white tank top and his hands tied in front of him, talking to the negotiators. At one point, when Spitzer tried to give the negotiators some information that the terrorists did not want them to have, one of the terrorists clubbed Spitzer in the head with the butt of an AK-47 assault rifle and pulled him away from the window. That was the last time most people saw Spitzer alive.
After 20 hours of tense negotiations, the hostages and terrorists were flown by helicopter to Fürstenfeldbruck airbase where, the terrorists believed, they would be flown by jet to a friendly Arab nation. Instead, the Bavarian border patrol and Munich police attempted an ill-prepared ambush/rescue operation. After a fierce two-hour gunfight, Spitzer watched helplessly as four of his teammates were executed with machine guns, then incinerated when a grenade was detonated inside their helicopter. Seconds later, Spitzer and four more of his teammates were then fatally shot by the terrorists. Five of the terrorists and a Munich police brigadier were also killed in the gunfight.
Spitzer was buried alongside teammates Amitzur Shapira, Kehat Shorr, Eliezer Halfin, and Mark Slavin at Kiryat Shaul Cemetery in Tel Aviv, Israel.
Despite having no family in Israel and knowing little Hebrew, Ankie Spitzer decided to remain in Israel with her daughter, and later converted to Judaism. Ankie explained that she thought that if she returned to Amsterdam to raise her daughter, "I would never be able to explain to Anouk what her father was about. She would always be an exception there. Here, she would fit in".
Ankie Spitzer confirmed that during Operation Wrath of God, an operation by Mossad (Israeli external intelligence) to track down and assassinate the masterminds of the Munich massacre, Mossad officials regularly called her home to inform her whenever a target was killed. Ankie claimed that she drew no satisfaction, and would have preferred for the terrorists to have been put on trial: "It didn't fill me with joy to think, 'Oh, great, now they're revenging Andre', because I never looked for that revenge. I don't live for revenge, I live for justice".
In 1980, Ankie Spitzer married Elie Rekhess, a professor at Tel Aviv University, and is now known as Ankie Rekhess-Spitzer. She led the fight to get the German government to admit their culpability in the failed rescue of Andre and the others. In 2003, a financial settlement was reached between the German government and the families of the Munich victims. Today she is a correspondent in Israel for Dutch and Belgian television.