He sought to begin his training at the Royal Danish Academy of Art (Det Kongelige Danske Kunstakademi) already in 1760 at the age of 11.
Sculptor Simon Carl Stanley took an interest in the child, and with his help Johan came into the School of Drawing in 1761.
He soon won another influential protector, theatrical painter Peter Cramer, who recommended him to sculptor Johannes Wiedewelt.
Clemens made etchings based on Wiedewelt's illustrations for a deluxe edition of Ludvig Holberg's "Peder Paars" in 1772, giving the youngster a decent income in which to support himself and his father.
He developed such a glowing reputation as an artist in Paris that the Academy soon offered to take him on as a member, provided he produced a new, quality work for his application piece.
He requested permission to stay, and was denied it because "certain important people" wanted Clemens to return to Copenhagen to etch plates for a royal project.
Clemens left Paris in 1777 along with Jens Juel and Simon Malgo, and traveled to Geneva, where he made vignettes for Charles Bonnet's "Oeuvres d'histoire naturelle et de philosophie " and an etching based on Jens Juel's portrait of Bonnet.
The portrait drew a lot of attention to Clemens' skills, and led to a lifelong collaboration between the two artists.
Clemens' 1780 illustration for the first volume of Ewald's work— for the dramatic piece "Adam and Eve"— was considered indecent, and led to a break in their collaboration for several years.
Clemens occupied a central position in that time's artistic life and spirit, and was an avid participant in the Enlightenment's scientific and philosophical discussions.
In 1787 Clemens was invited to Berlin to make an etching based on a drawing by Englishman E.F. Cunningham, "Frederick the Great Riding Home After Manoeuvres at Potsdam".
In 1789 his engravings based on Abildgaards originals appeared in another Ludwig Holberg work "Niels Klim".
When the Berlin assignment was completed Clemens traveled in 1792 with royal permission to London to work on a new etching based on John Trumbull's The Death of General Montgomery in the Attack on Quebec, December 31, 1775.
His engraving "Slaget på Reden" (The Battle of Copenhagen) was created in 1801, and was based on a drawing by Christian August Lorentzen.
He won himself many loyal supporters and good friends early on, among them two of the most important Danish artists of his time, Jens Juel and Nicolai Abraham Abildgaard, who were vital for him as an aspiring young engraver.