'dismissable' originates from English, specifically formed from the verb 'dismiss' plus the adjectival suffix '-able' (from Latin '-abilis' via Old French), where '-able' meant 'capable of or susceptible of'.

'dismiss' changed from Old French forms (for example 'desmettre' / 'dismettre') and ultimately from Latin 'dimittere' (dis- + mittere), and eventually became the modern English 'dismiss'; the adjective was created in English by adding '-able'.

Initially, the Latin root 'dimittere' meant 'to send away' or 'to let go'; over time in English it evolved to mean 'to remove from office, to reject, or to let go', and the adjective 'dismissable' developed the current sense 'capable of being dismissed or set aside'.