Andrea Reeb had been under fire from Alec's legal team, with his defense calling for Reeb to step down because Baldwin's camp has argued that her trying the case while also being a state legislator in New Mexico violates the state’s constitution.

Well, Alec and co. got their wish Tuesday, when Reeb announced she was stepping down from prosecuting him.

In a statement to TMZ, Reeb says ... "After much reflection, I have made the difficult decision to step down as special prosecutor in the 'Rust' case. My priority in this case -- and in every case I’ve prosecuted in my 25-year career -- has been justice for the victim."

Reeb adds ... "However, it has become clear that the best way I can ensure justice is served in this case is to step down so that the prosecution can focus on the evidence and the facts, which clearly show a complete disregard for basic safety protocols led to the death of Halyna Hutchins."

The challenge from Alec's legal team was also referenced, with Reeb ending her statement by saying ... "I will not allow questions about my serving as a legislator and prosecutor to cloud the real issue at hand."

The office of New Mexico's First Judicial District Attorney tells us official paperwork has been filed with the court to formally remove Reeb as special prosecutor.

Reeb stepping down is a huge development ... there have already been some miscues by the prosecution, with Baldwin's lawyers recently getting the D.A. to drop the gun enhancement charge against him.

Alec's still charged with involuntary manslaughter in the death of Hutchins ... and last month he pled not guilty.