To propagate any flower that grows from a corm, dig the plants when….

They are dormant (summer for crocus, fall for most other corms). Many plants that grow from corms are not very winter hardy, including gladiolus. These are usually stored through winter like dahlias. Before replanting them, break off and discard old, shriveled corms and the little cormels. This should leave you with one fat new corm ready for replanting.