He competed for Switzerland at the 1964 Winter Olympics, placing 24th. He retired from competitive skating following that season. As a skater, Grütter was coached by Jacques Gerschwiler.
Grütter began coaching in 1965.
His most notable student has been Stéphane Lambiel, whom he coached from 1995 until June 2008 and again from July 2009. Others among his current and former students include Noémie Silberer, Kristel Popovic, Raphaël Bohren, Samuel Contesti, Laurent Alvarez Paolo Bacchini, Alisson Perticheto, and Anna Ovcharova.