除外
じょがい · jogai · JLPT N1 · noun
exception
除 = remove, 外 = outside: exclusion removes something to the outside
Both kanji are common on their own: 除 (remove, divide) and 外 (outside). 除外する is the verb form, meaning to take something out of a set. In rules, 除外 is close to 例外 (exception).
除 — left ear/mound 阝 + surplus 余
除 combines the 'mound/steps' radical 阝 (originally 阜, a hill) with 余 as the phonetic. It first meant the steps of a palace, then extended to 'remove' or 'clear away' (as one sweeps steps clean), and later to mathematical 'divide.'
外 — evening 夕 + divination 卜
Originally a compound of 夕 (evening) and 卜 (divination). Ancient Chinese divinations were performed in the morning; doing them at evening (夕) was considered irregular or 'outside' the norm. From this sense of deviation, 外 came to mean 'outside' or 'external'.