Burr, 58, took charge in May following spells at Stalybridge, Southport, Chester and Kidderminster.
A statement from the board read: "It is with regret that today we have accepted the resignation of our manager Steve Burr.
"We would like to thank Steve for all his hard work and passion during the last few months.
"He has worked tirelessly from the start , building a new team from scratch and we would like to wish him all the best in the future."
Assistant manager Andy Fearn and first team coach Alex Meechan will continue running the team with the club expected to make a further statement soon.
Burr said: "I have taken the decision to resign from Stafford Rangers. I would like to thank the Board of Directors for all their support during my short time at the club.
"It has been a tough year on a personal note. I would like to wish everyone connected with the club all the very best for the future."
Burr's last game in charge was a 4-1 home defeat to league leaders Nantwich Town on Boxing Day.
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