Per Derksen, *mamiti is from *mȃmъ(“deceit”) + *-iti, from Proto-Indo-European*meh₂-mo-, from the root *(s)meh₂- that also underlies Proto-Slavic*majati(“to wave, to beckon”), *mavati(“to wave, to beckon”), *māxàti(“to wave”). See *majati for further etymology. Derksen believes (following a theory of Van Wijk) that the synonymous verb *maniti developed from *mamiti by dissimilation, under the influence of *manǫti(“to beckon”), and that the Baltic cognates Lithuanianmõnyti(“to practice sorcery”), Latvianmãnît(“to deceive, to mislead”) are both borrowings from Slavic.
Chernykh, P. Ja. (1993) “мани́ть”, in Историко-этимологический словарь русского языка [Historical-Etymological Dictionary of the Russian Language] (in Russian), 3rd edition, volume 1 (а – пантомима), Moscow: Russian Lang., →ISBN, page 508
Vasmer, Max (1964–1973) “мани́ть”, in Oleg Trubachyov, transl., Этимологический словарь русского языка [Etymological Dictionary of the Russian Language] (in Russian), Moscow: Progress