A native of Birmingham, Alabama, Grammas played in Major League Baseball (MLB) for the St. Louis Cardinals, Cincinnati Redlegs and Chicago Cubs.

During his third season in the ChiSox' farm system, he was acquired by Cincinnati in 1951 and continued his minor league apprenticeship in the Reds' organization.

Loaned to the New York Yankees' Kansas City Blues affiliate in 1953 (Cincinnati at the time lacked a Triple-A farm team), Grammas collected a career-high 179 hits and batted .307.

In 1964, Grammas began his managing career as skipper of the Cubs' Double-A affiliate, the Fort Worth Cats of the Texas League.

He began his big-league managerial career when he was asked finish out the Pirates' 1969 season after Larry Shepard was fired as the team's manager on September 26.

After the Milwaukee Brewers fired Del Crandall as manager near the end of the 1975 season, his place was taken on an interim basis by Harvey Kuenn.

Only the expansion 1977 Toronto Blue Jays, who lost 107 games in their inaugural season, kept the Brewers from consecutive last-place finishes under Grammas.

[3][4] A 10–5 start in 1976 led Sports Illustrated to publish a story praising Grammas' positive attitude and mental approach to the game.