"Mutie" was a derogatory term for people on the planet Barrayar who were genetically defective or had an obvious mutation.
The closing of the original wormhole to Barrayar produced radiation that often caused mutations in human babies on the planet. Further, the initial settlers had trouble with mutagens in their environment, resulting in the "Mutagen Disasters". The need to deal with this problem while simultaneously trying to survive on a hostile planet while cut off from the rest of Galactic civilization resulted in the Barrayaran tradition of killing infants with obvious mutations. By the time of Emperor Gregor Vorbarra, killing mutants had been outlawed, though "muties" were still despised by many Vor and plebes for being genetically "impure".
Miles Vorkosigan was often called a "mutie" for being abnormally short and physically crippled.
Many Barrayarans would also have viewed Quaddies and hermaphrodites as "Muties".