Beeby, a lifelong Iron fan, has been at the club since 2001, initially running the official website before becoming the company secretary.
"Steve Wharton, the chairman, thanked Jamie Hammond for the contribution he had made over his six year tenure," read a statement from the club.
"With David's wealth of knowledge, gained over the last nine years at the club, he was confident the club would move forward."
Hammond's exit was the third of the day, following the departure of first-team regulars Paul Hayes and Marcus Williams after they rejected new contracts.