Taseff had an 11-year playing career, primarily with the Baltimore Colts, where he was a member of the 1958 and 1959 NFL Championship winning teams.

Taseff attended East High School in Cleveland, Ohio, where he played football and basketball.

[1] Taseff was used sparingly as a rusher and receiver on offense and an occasional kick return man, as the Browns finished the season with a 11—1 win–loss record and advanced to the 1951 NFL Championship Game, which they lost to the Los Angeles Rams.

[3][4] The Browns released Taseff on waivers prior to the regular season, but he went unclaimed and the team added him to the roster when halfback Don Phelps was injured.

[6] Joining Taseff in making the move from the Browns to the expansion Colts were such future starters as defensive backs Don Shula and Bert Rechichar, end Art Spinney, and veteran guard Ed Sharkey.

[3] After retiring as a player, Taseff became a defensive backs coach with the Boston Patriots of the American Football League.

Taseff was a member of the Dolphins coaching staff during their 1972 perfect season, which ended in a victory against the Washington Redskins in Super Bowl VII.

Taseff coached running backs such as future Pro Football Hall of Fame member Larry Csonka, Jim Kiick, and Mercury Morris.