'blastic' originates from Greek, specifically the word 'blastos', where 'blastos' meant 'bud' or 'germ'.

'blastic' entered English via Neo-Latin/medical coinage (e.g. 'blasticus') based on Greek 'blastos', and was adopted in technical/medical contexts as 'blastic'.

Initially it meant 'pertaining to a bud or germ' in biological senses; over time it retained that technical sense (relating to blast or blast cells) and has also been used metaphorically/briefly in contexts referring to explosive blasts or blast-related damage.