Hinkie joined the Sixers three years ago and has presided over the NBA's worst ever record of 47-195 since he took the job, including a joint record of 18 consecutive losses to start a campaign this term.
In a 13-page letter to the Sixers' board obtained by ESPN, Hinkie wrote: "Given all the changes to our organisation, I no longer have the confidence that I can make good decisions on behalf of investors in the Sixers - you. So I should step down. And I have.
"There has been much criticism of our approach. There will be more. A competitive league like the NBA necessitates a zig while our competitors comfortably zag. We often chose not to defend ourselves against much of the criticism, largely in an effort to stay true to the ideal of having the longest view in the room."
In a statement, Sixers managing general partner Josh Harris said: "While we are disappointed in Sam's decision, we would like to sincerely thank him for his contributions over the past three seasons. There is no question that Sam's work has put us in a very strong position to take advantage of numerous opportunities for an exciting future."
Former Toronto Raptors GM Bryan Colangelo is thought to be in advanced talks to succeed Hinkie.