His brother, Joseph Kutter (1894–1941), became one of Luxembourg's foremost painters, while Bernard (1889–1961) also became a photographer.
Edouard began working as an apprentice with his father in 1898 before studying photography at some of the most highly developed studios in Germany and Austria.
After managing a branch of his father's business for a few months in 1917, he opened his own studio at 4, avenue de la Liberté, in 1918.
The same year, Grand Duchess Marie-Adélaïde gave him the title of court photographer.
As a result, he took many photographs of the Grand Ducal family, which can be viewed today in Luxembourg's Photothèque.