The House Ethics Committee announced earlier this month that it is investigating accusations that Miller physically abused his ex-wife and daughter. Miller denies the allegations.
The departure of Dan Driscoll, who at one time was viewed as a potential replacement for the defense secretary, marks the latest shake-up at the Pentagon.
The vice president is set to appear at a Republican Jewish Coalition summit at a time when many prominent donors and activists oppose his potential presidential bid.
The decision hands President Donald Trump a major political victory in his controversial bid to oversee the largest addition to the executive mansion in decades.