9:02 AM -- Tamar's rep tells TMZ the singer made an "extremely difficult decision" in filing for divorce. The rep adds, "Collectively, their son Logan and his well being during this very unfortunate process is most important.

Tamar Braxton is done with her marriage ... she's filed to divorce Vincent Herbert ... TMZ has learned.

Tamar filed divorce docs Tuesday in L.A. County. She and Vincent have been married for nearly 9 years -- they're one month shy of their anniversary. Tamar and the record exec have one child together -- their 4-year-old son, Logan Vincent.

It's the end of a long relationship -- Tamar and Vincent started dating in 2003. Her sister, Toni Braxton, had been working with him and introduced them.

The couple had a domestic dispute in August, 2016 in an Atlanta hotel. Police were called after he allegedly bit her hand during the argument.

Although they stayed together after that ... sources connected to the couple tell us it's been a rollercoaster relationship, and Tamar recently moved out of the family home.

Story developing ...