'aseptate' is formed from the privative prefix 'a-' (from Greek, meaning 'not' or 'without') attached to 'septate', which derives from Latin 'septum' meaning 'a fence or partition'.

'septum' (Latin) gave English 'septum' and the adjective 'septate' ('having septa'); the adjective 'aseptate' was created by adding the privative 'a-' to 'septate' to indicate 'without septa'.

Initially the elements meant 'not' + 'having partitions'; the combined word has retained that specific biological meaning of 'without septa' in modern usage.