'mimickingly' ultimately traces back to Greek, specifically the word 'mimos', where 'mimos' meant 'imitator' or 'actor'.

'mimos' passed into Latin as 'mimicus' and into Old French as 'mimique'; from these came Middle English 'mimic', which produced forms such as 'mimicking' and the adverbial form 'mimickingly' in later English.

Initially it referred to 'an imitator' or 'actor' (one who mimics); over time the verb sense 'to imitate' developed, and the adverbial sense evolved to 'in an imitative (often mocking) manner', which is the modern usage.