The chemical reactions and pathways occurring at the level of individual cells resulting in the breakdown of biogenic amines, any of a group of naturally occurring, biologically active amines, such as norepinephrine, histamine, and serotonin, many of which act as neurotransmitters. [ GOC:jl http://openisbn.com/search.php?q=0198506732&isbn=1/ GOC:go_curators ]