[2] The native of Huntsville, Alabama, batted left-handed, threw right-handed, and was listed as 6 feet 3 inches (1.91 m) tall and weighed 205 pounds (93 kg).
He was a member of the last editions of each of Washington's two 20th Century American League teams and their first-year squads in their new locales, Minneapolis–Saint Paul (1961) and Dallas–Fort Worth (1972).
[8] Mincher's professional baseball career began when he signed as an amateur free agent with the Chicago White Sox after graduating from Huntsville's S. R. Butler High School in 1956.
[10] He steadily rose through the Chicago system over four years, but was traded to Washington on the eve of the 1960 season (April 4, 1960), along with young catcher Earl Battey, and $150,000 for veteran Senators' slugger Roy Sievers.
[10] He made his major league debut on April 18, 1960, as cleanup hitter and first baseman for the Senators; batting between Harmon Killebrew and Bob Allison.
Mincher had his franchise high in plate appearances (497) and games (139), repeating his .251 batting average from 1965; but his home runs fell to 14, and RBI total to 62.
[3][20] After the season was over, the Twins traded Mincher, Jimmie Hall and Pete Cimino to California Angels in exchange for Dean Chance and a player to be named later (Jackie Hernandez).
[3] Mincher was hit in the face by a pitch from Cleveland Indians pitcher Sam McDowell during the season, leading to headaches and dizziness and affecting his quality of play and availability.
[27] Despite his successes, Mincher was traded by Brewers before their first season, along with Ron Clark, to the Oakland Athletics for Phil Roof, Mike Hershberger, Lew Krausse and Ken Sanders.
[3] In May of the following season, the A's traded Mincher with Frank Fernandez, Paul Lindblad and cash to the Washington Senators (the expansion team created in 1961)[28] for Mike Epstein and Darold Knowles.
[3] The Senators became the Texas Rangers in 1972,[28] where he played in 61 games before being traded back to the A's with Ted Kubiak for Marty Martinez, Vic Harris and a player to be named later (Steve Lawson).
[9] His playing career ended after the 1972 season, which saw the 34-year-old Mincher hit only .148 with 5 RBI in 47 games, mostly as a pinch hitter, after Oakland reacquired him from the Rangers on July 26.
[7] But in the 1972 World Series, Mincher's ninth-inning pinch single in Game 4 off Clay Carroll drove home the tying run, as the Athletics came from behind to defeat the Cincinnati Reds, 3–2.
[29] Mincher's name appeared in the box scores of two other games, but he never officially batted in either contest when he was replaced by a right-handed pinch hitter.
[4][6] On June 9, 1966, in the seventh inning of a game against the Kansas City Athletics, Mincher was one of five Twins players to hit home runs.
[35] Mincher was one of only 21 players to hit a home run completely over the right-field roof and out of Tiger Stadium in Detroit during the 64-year history of its final configuration.