Konstantin Apollonovich Savitsky was born in 1844 in Taganrog to a military doctor and began his education at the Taganrog Classical Male Gymnasium. After the early death of his parents, his relatives sent him to a private boarding school at the Livonian Noble Gymnasium in the village of Birkenrue. In 1862, after completing his studies, Savitsky entered the Imperial Academy of Arts, where he studied historical painting under professors F. A. Bruni, A. T. Markov, and P. P. Chistyakov.

At the Academy, Savitsky received seven medals for his works: in 1868, three small silver medals for the painting "The Street Musician"; in 1869, a large silver medal for the sketch "The Crucifixion of Christ"; in 1870, a large silver medal and a large encouragement medal for the paintings "The Visit to the Sick Son" and "The Watchman at the Powder Magazine". In 1871, for the program "Cain and Abel," he was awarded a small gold medal and sent abroad by the Academy, where he received a scholarship from Emperor Alexander II until 1874. During this time, he attended art academies in Dresden and Düsseldorf, lived in Paris, and became interested in metal engraving.

From 1872, Savitsky became an exhibitor, and from 1878, a member of the Society of Traveling Art Exhibitions. In 1878, he participated in the World Exhibition in Paris, and in 1882, in the All-Russian Art and Industry Exhibition in Moscow.

After the tragic death of his wife in February 1875, Savitsky returned to Russia and settled in Dvinsk, where he created several significant works, such as "The Meeting of the Icon" in 1878 and "To War" in 1880.

From 1883 to 1889, Savitsky lived in St. Petersburg and taught at the Central School of Technical Drawing of Baron A. L. Stieglitz. In 1891, he moved to Moscow, where he became a teacher at the Moscow School of Painting, Sculpture, and Architecture, and from 1894, he headed the life drawing class. In 1895, Savitsky became a full member of the Imperial Academy of Arts, and in 1897, he was awarded the title of academician of painting.

By the will of Lieutenant General N. D. Seliverstov, who was killed in Paris in 1890, 300,000 rubles and a collection of books and paintings were transferred to the city treasury of Penza with the condition of creating an art school. Savitsky was appointed the first director of the Penza Art Gallery and the Penza Art School named after N. D. Seliverstov, which opened in 1898. He developed the curriculum and made changes to the building layout, and the best graduates of the school were admitted to the Imperial Academy of Arts without exams. Thanks to Savitsky, traveling art exhibitions were sent to Penza in 1898 and 1901.

Savitsky headed the school until his death on January 31, 1905, and was buried at the Mitrofanovskoye Cemetery in Penza. Streets in Penza, the Penza Regional Art Gallery, and the Penza Art School are named after him. A memorial plaque honoring the outstanding painter is installed on the school building. In the 1980s, a memorial museum of Savitsky was established in the Penza Regional Art Gallery, and in 2011, a monument to the painter was erected in Penza.