Rasmussen pitched in the Major Leagues from 1975-1980, and again from 1982-1983. In late & , Rasmussen pitched in the Mexican League. He also pitched for the Fort Myers Sun Sox for the duration of the two-year run of the Senior Professional Baseball Association.
Rasmussen accepted a pitching coach position in the Cleveland Indians' minor league system in . In , he jumped over to the Minnesota Twins' oganization, where he has remained ever since. From 1991 through he was the pitching coach for the Rookie level Gulf Coast League Twins, in and , he coached the Twins' advanced A affiliate, the Fort Myers Miracle, in he jumped to the Double A New Britain Rock Cats, and in , he returned to the Miracle.
Some of the more notable names to have been coached by Rasmussen include Johan Santana, Francisco Liriano, LaTroy Hawkins & Mark Redman.