Was Mulligan a really bad golfer that they named it after him?
JE Lighter American Slang shows the first printed use of the term as relates to golf in a 1949 cite.
He lists the term Mulligan as referring derisively about an Irish person as early as 1874, inferring that a mulligan was a stupid Irishman.
In a 1970 golf encyclopedia, he says mulligan is similar to a shapiro!
Not hard to extrapolate that giving an opponent a second shot after they blew the first one might come to have a derrogatory slang origin.