Saabye was born in Skivholme, , Aarhus, the son of vicar Erhard Saabye (1778-1851) and Susanna Schmidt (1785-1856).
He competed as an individual for the Neuhausen Prize in 1854 and although he did not win, his work was praised so that he obtained the support of Herman Wilhelm Bissen and his father's permission to take up sculpture.