Mazer’s family left Kiev, emigrating before his first birthday. He grew up in Brooklyn, New York. A graduate of Yeshiva University High School for Boys, he received a BA at University of Michigan for premed before being drafted. During World War II, he served the majority of his time in the Armed Forces-Air Force Transport Command in the Pacific theatre.  After returning home, he married Dora Sudarsky (“Dutch”), his pre-war sweetheart. They had three children. Their marriage lasted 50 years until Sudarsky’s death from cancer on April 28, 1996. The New York Knickerbockers observed a moment of silence during their May 1, 1996 Playoff game. Mazer never remarried.  Mazer’s broadcasting career began in 1942, broadcasting in Grand Rapids, Michigan before joining the United States Military that same year.

His career as a sportscaster began in Buffalo, New York in 1947, where he signed on as a sportscaster on WKBW. In 1947, he was also the commercial announcer on the CBS William L. Shirer Newscast, as well as the commercial announcer for the soap opera, When a Girl Marries. By 1948, he had also became the sports director for WGR radio and served as principal sports anchor for WGR-TV from the time that station signed on in 1954 through the early 1960s. Mazer dominated the airwaves in Buffalo, broadcasting the hockey and baseball Buffalo Bisons, the All-American Football Conference Buffalo Bills and Little 3 Basketball. With years of play-by-play and sports commentary in Buffalo under his belt, Mazer arrived in New York City in 1964 when WNBC (AM) went to its first all-talk format. His show was one of the pioneer examples of the modern sports talk show in America.  After filling in for Hugh Downs on the NBC game show Concentration, he was given his own show, Reach for the Stars, in January 1967, but the show was quickly cancelled.

Mazer served as a color analyst and intermission host, working alongside Dan Kelly on CBS’ National Hockey League coverage from the late sixties until the early seventies, broadcasting the Stanley Cup playoffs a few times. Golf was another Mazer specialty on NBC, including the U.S. Open and Bing Crosby tournaments in the mid-1960s. ABC used Mazer for its regional New York football lineup in the late 1960s. Mazer also did sideline reporting for CBS coverage of the NFL in the late 1960s.  During the 1960s and 1970s, Mazer did much voice-over commercial work, from L&M Cigarettes, Kodak, Ford automobiles to Trident chewing gum, among many others.

Mazer was a sportcaster at New York’s WNEW-TV (Metromedia Channel 5) for twenty years, ending in the early 1990s. He also co-hosted the program Sports Extra, which originally teamed him up with Lee Leonard and then later with Brian Madden (1976–78), respectively. Sports Extra is also considered to have been the first “sports wrap-up” show of its kind.  While doing sports for The 10 O’Clock News on WNEW in the late 1970s and ’80s, he held a daily contest where a viewer would send in a question to “stump” Bill and would win a prize if he or she did. Usually the submitted question was asked by anchorman John Roland.

Mazer hosted a WFAN sports show from Mickey Mantle’s restaurant from 1988 to 1991, and returned to the station on June 30, 2007 to host an hour long show from 10–11 AM during the station’s 20th anniversary celebration and reunion weekend. He was also a morning talk show host on WEVD, where he expanded to a comprehensive liberal talk format from 1992 to 2001. The show ended when WEVD was optioned to ABC’s ESPN division and became sports station WEPN.  Bill Mazer has appeared on the cable TV show The Leon Charney Report, as well as minor parts in movies such as Eyewitness, Raging Bull and appearing in episodes of ESPN SportsCentury as an expert on sport figures including Gordie Howe, Lawrence Taylor and Mickey Mantle.

Following his departure from WEVD in 2001, Mazer launched an afternoon interview program on WVOX in New Rochelle, New York from 3–6 PM EST (available via streaming from WVOX’s website), with his son, Arnie Mazer, serving as producer. His last show on WVOX was aired August 3, 2009, ending his tenure at the station after nearly eight years.  Mazer’s death was reported on October 23, 2013 at the age of 92. He died at a hospital in Danbury, Connecticut.