Born in Bonn, Germany, into a family of Jewish ancestry, Kuttner was raised as a Lutheran and converted to Roman Catholicism in 1932.
Two years later he fled Nazi Germany for Italy, where he worked as a research fellow at the Vatican Library and taught at the Lateran University in Rome.
Kuttner had a large family and at the time of his death was survived by his wife, Eva (née Illch), eight of nine children, twenty grandchildren, 14 great-grandchildren and a sister.
Kuttner also founded the publishing series Monumenta Iuris Canonici and the journal Bulletin of Medieval Canon Law.
Kuttner was recognized for his life's work by his 1969 induction into the prestigious Order Pour le Mérite, Germany's highest honor to bestow on artists, scholars, and scientists.