The Robins were relegated to the bottom tier of English football after a dismal 2016/17 campaign.
Sherwood was appointed in the role last November on the request of owner Lee Power, who is a close friend. In April, the 48-year old revealed that he was not receiving payment for the job.
Swindon unveiled their new manager, David Flitcroft, on Wednesday, and Power was asked about Sherwood.
"Tim's gone," replied Power.
And Power issued a similar response when asked about the director of football role.
"That's gone," he added.