Mayuko Toyota, a 42-year-old Harvard graduate and up- and-coming member of the ruling Liberal Democratic Party (LDP), can be heard screaming at the unnamed aide, saying he should die as she mocked his thinning hair.
Her 55-year-old secretary can be heard repeatedly apologising and begging the lawmaker to stop kicking and beating him.
"Don't damage my reputation anymore," Toyota screams, apparently in response to a mistake she claims the man had made.
The secretary recorded the exchange, which took place last month inside a car that he was driving, according to a weekly magazine that was given the tape and uploaded on YouTube.
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The magazine wrote a story that claimed Toyota had threatened to crush the man's head with a pipe in a separate incident, and made references to the hypothetical rape and murder of his daughter.
An LDP official said Toyota submitted a letter of resignation on Thursday, but it was not clear if it would be accepted.
The incident marks the latest in a string of scandals involving younger LDP members, including one who quit over an extramarital affair and another who quit over his financial dealings.