Dempster confirmed the details after a meeting with owner John Radford and separate, individual meetings with the players on his first full day in the job.
Bobby Olejnikm and Jason Law have both verbally accepted new deals while negotiations are underway to keep Jacob Mellis and Ben Turner.
Stags had a contract option on keeper Conrad Logan and have exercised that and retained his services for 2019/20.
Players already under contract for next season and retained are: Hayden White, Mal Benning, Matt Preston, Krystian Pearce, Alex MacDonald, Neal Bishop, Craig Davies, Otis Khan, Willem Tomlinson, Ryan Sweeney, CJ Hamilton, Omari Sterling-James, Lewis Gibbens, Jordan Graham, Alistair Smith, Danny Rose, and Jimmy Knowles.
Loan players returning to their parent clubs are: Jordan Smith (Nottingham Forest), Tyler Walker (Nottingham Forest), Gethin Jones (Fleetwood Town), Nicky Ajose (Charlton Athletic) and Jorge Grant (Nottingham Forest) Meanwhile, defender David Mirfin has announced his retirement from football after his injury problems.