The 28-year-old Nottingham-born player has been at The Brit Oval since 2004 but has decided to terminate his contract.
Surrey cricket manager, Alan Butcher, said; "It's not unusual for a professional sportsman to be left out of a team."
"They dont enjoy it but on most occasions they take it on the chin and fight to regain their place as Alastair Brown has vowed to do."
"Its a pity that Nayan is unwilling to do this as he was part of our future plans but in the position we find ourselves in, we need people who are prepared to take on a challenge."
"This appears to be no longer the case and so I have accepted his resignation. As a club, we wish him all the best in the future."
With the emergence of leg-spinner Chris Schofield and the recent signing of Harbhajan Singh for the rest of the season, Doshi has been unable to command a regular place in the Surrey side.
Doshi claimed he did not want to fall out with the club but was unhappy with his lack of first-team action.
"I regard myself as a good spin bowler and I just didnt feel that I had the backing that I should have had.
It is for this reason that I have decided to step down. There are no bad feelings as this was my decision and I wish the club the best of luck for the remainder of the season," he added.
Doshi, son of former India spinner Dilip Doshi signed a two-year deal with the club at the end of 2006.