He lived his entire life in Zurich. Nothing is known of his life until 1526, when he married the daughter of Ludwig Nöggi, a master carpenter who sat in the city council, and his first artwork dates only from 1531. Asper was himself a citizen of some standing, and was elected to the Great Council in 1545.
He painted in a variety of styles, and is particularly known for his studies of flowers and fruit. Many of his pictures are lost. His portraits show affinity to the works of Hans Holbein. Notable works include portraits of Huldrych Zwingli and Zwingli's daughter Regula Gwalter, which came into the ownership of the public library of Zurich. Asper is also believed to have provided the illustrations for Conrad Gesner's Historia Animalium.