He didn't get along well with his higher-ups, either. Reports are he blew up at Branch Rickey while on Pittsburgh's roster in 1955, which sent him to Hollywood for the season, then optioned to independent El Paso. It was from there that he was sold/waived to the Giants for 1956, that transaction is on his Baseball-Reference page.
Mangan didn't think much of Bill Rigney's management style (Mangan had managed at El Paso in 1955) and got himself suspended. From the Aug 14, 1956 Billings Gazette:
"Jim Mangan, third string catcher of the New York Giants, who said Manager Bill Rigney "is the worst manager I ever played (for)" Monday was was suspended indefinitely by Club President Horace Stoneham "Mangan is suspended as of today until further notice hecause of his act in leaving the club at Pittsburgh," Stoneham's notice read. No mention was made of the 25-year-old sub's reason to newspapermen. Mangan, who was purchased from Pittsburgh, left at the end of the 2nd inning of the first game of a doubleheader with the Pirates, telling Rigney he could not "stand it any more." He stayed away from the park during the entire second game but returned to New York with the team. The San Franciscan has seen little action this season. Bobby Bragan, manager of the Pirates, said "This follows a pattern. This fellow told off Branch Rickey last year." Following this blowup, Mangan, who was owned by the Pirates and was playing for Hollywood in the Pacific Coast League, was sent down to El Paso in the WestTexas-New Mexico League. Mangan batted .245 for Holly- wood last year."
Mangan never played in the majors again, and came back in the season only to be used as a bullpen catcher for the Giants that year. In 1957, Mangan goes to the Sacramento PCL independent team in a deal not on his Baseball-Reference page. From the Pasadena Star-News of March 23, 1957:
“Sacs Buy Receiver From N.Y. Stormy Catcher Jim Mangan today became Sacramento's headache as the Solons' front office announced that he has been purchased for an undisclosed sum from the New York Giants. Mangan is the boy who called Bill Rigney, New York Giants skipper the worst manager n baseball last year and left the club in a huff, was suspended and eventually was allowed to rejoin the team and used in the bull pen only. This spring Mangan, who formerly played with Hollywood and had a few run-ins, as well, was assigned to Minneapolis, the Giants' farm club, now training at Stanford, Fla. Mangan will stop at Minneapolis to pick up his car and drive to Pasadena, being ex- pected next week. He played in 20 games for New York and hit .100.”
Mangan played sparingly for the Solons as third string catcher, then went to AA San Antonio and the Orioles system in 1958 despite going to spring training for the Solons. There is evidently one game for Fort Worth and the Cubs system in 1957 that I can't track down.
One thing about the majors back then, if you hit less than .200 and criticized management, your career tended to disappear.