TMZ Sports has obtained court docs which show Mat's ex-girlfriend went to authorities in Florida to report several incidents in which she claims Mat physically and emotionally abused her ... dating back to 2017.

According to court docs, the woman claims the first incident occurred back in Sept. '17 -- when Mat got angry and flipped over a bed while she was still on it.

"He tackled me to the floor, picked me up and slammed me on the couch where he got on top of me pressing his forearm on my throat."

The woman claims Latos then backed her into a wall and told her, "I'll f**king kill you."

"He then spit on me, put water in his mouth and spit more."

She claims the abuse continued in January 2018 -- when Latos locked her in her closet.

In April 2018, the woman claims Latos slashed her tires with a knife. She reported that incident to police.

In August 2018, the woman claims Latos got violent again -- but this time she hit back, elbowing him in the jaw. She claims a witness will back up her account.

The woman claims she's in fear for her life -- especially since Latos owns "multiple guns."

A judge granted a restraining order on August 28 requiring Latos to keep at least 500 feet from the woman at all times -- and it's been extended until October when the case is due back in court.

We reached out to Latos for comment. So far, no word back.

30-year-old Latos was a stud during his 9 seasons in the Big Leagues -- striking out more than 1,000 batters while playing for the Reds, Padres, Blue Jays and other teams.