'mitochondria-associated' is a compound formed from 'mitochondria' and 'associated'. 'Mitochondria' comes from Modern Latin/Greek 'mitochondrion' (plural 'mitochondria'), and 'associated' derives from Latin 'associatus' (past participle of 'associare').

'Mitochondrion' was coined in Modern Latin from Greek elements 'mitos' meaning 'thread' and 'khondrion' meaning 'small granule'; it entered English scientific usage in the late 19th to early 20th century as 'mitochondrion' (plural 'mitochondria'). 'Associated' came into English via Old French/Latin 'associare' → Medieval/Modern Latin 'associatus' and meant 'joined or connected'. The compound 'mitochondria-associated' is a recent English formation combining the established scientific noun with the past-participial adjective 'associated'.

Individually, 'mitochondrion/mitochondria' originally named a cellular structure ('thread/granule') and has retained that biological sense; 'associated' originally meant 'joined or partnered' and has retained the sense of being connected. Together the compound now specifically denotes a physical or functional connection to mitochondria.