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:go_curators GOC:jl https://www.worldcat.org/search?q=bn%3A0198506732 ]