Saville, 25, joined the Shots from Barnet last summer and made 26 appearances in all competitions.
Walker, 26, scored 14 goals in 40 league appearances after moving to the EBB Stadium from Luton.
Aldershot, who finished 15th in 2015-16, reappointed Gary Waddock as manager last month.
Aldershot Town defender Jack Saville and striker Charlie Walker have signed new one-year deals with the National League club.