Rebecca Tinucci, senior director of the electric vehicle maker's Supercharger business, and Daniel Ho, head of new products, will leave on Tuesday morning, The Information reported.
In the email, Musk also said he would dismiss everyone working for Tinucci and Ho, including the roughly 500 employees who work in the Supercharger group, The Information said.
"Hopefully these actions are making it clear that we need to be absolutely hard core about headcount and cost reduction," Musk wrote in the email, the report said. "While some on exec staff are taking this seriously, most are not yet doing so."
Tesla's public policy team, which was led by former executive Rohan Patel, will also be dissolved, according to the report.
Tesla did not immediately respond to Reuters' request for comment.
Earlier this month, Tesla ordered the layoffs of more than 10% of its global workforce, as it grapples with falling sales and an intensifying price war for electric vehicles (EVs).
Two senior leaders, battery development chief Drew Baglino and Patel also announced their departures, drawing posts of thanks from Musk although some investors were concerned.
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