A bottom hole assembly for use in a subterranean well can include a whipstock, a mill releasably secured to the whipstock, an antenna, and a release mechanism configured to release the mill from the whipstock in response to a predetermined radio frequency signal received by the antenna. A method can include positioning a bottom hole assembly in a well, the bottom hole assembly including a mill and a whipstock releasably secured to the mill, and then releasing the mill from the whipstock by displacing a radio frequency identification tag into the bottom hole assembly. A well system can include a bottom hole assembly comprising an anchor, a whipstock and a mill, and a radio frequency identification tag displaceable with fluid flow into the bottom hole assembly.p