Şevket Dağ was born in Istanbul and graduated from the School of Fine Arts in 1897. He spent the next twenty-three years teaching art at several schools, including the Royal School (today Galatasaray High School) and the Teacher Training School. He was one of the founders of the Ottoman Society of Painters in 1909, and served on the board of the society. His works were shown at the Galatasaray and Ankara exhibitions. He participated in exhibitions in Athens in 1904, Munich in 1909, Sofia and Brussels in 1910, Paris in 1933 and New York in 1939, and was awarded numerous prizes and medals. In the later part of his life he was elected as Member of Parliament for the provinces of Konya and Siirt.
The Ottoman Society of Painters was established in 1909 by a group of artists who included Şevket Dağ, Ruhi Arel, Sami Yetik, Hikmet Onat and İbrahim Çallı, under the patronage of the last Ottoman caliph Prince Abdülmecid Efendi (1868-1944), who was himself a painter. The society was an independent body that came into being in the new liberal atmosphere following the proclamation of the Second Constitution in 1908. It was dedicated to spreading interest in art and awareness of painting as a profession in Ottoman society. Later on artists such as Feyhaman Duran, Hüseyin Avni Lifij and Müfide Kadri joined the society, which was the first professional association of artists in Ottoman Turkey.