Det. Sgt. Steve Ryan says Allen Lascelles, 51, is charged with first-degree murder in the death of 31-year-old Suraiya Gangaram on Friday.
Ryan says Lascelles dated Gangaram on and off for two years before the relationship ended in 2014 after Lascelles was arrested and charged with domestic assault.
Lascelles was released in September 2014 under conditions not to contact Gangaram, but Ryan says the two had agreed to meet on Friday so that some property could be returned to him.
Police don't know exactly when the stabbing occurred, but say Gangaram's young daughter found her mother lying on the kitchen floor and called 911.
Ryan says that about 30 minutes after the girl found Gangaram, Lascelles attempted to jump in front of Via train but survived his injuries and is in hospital.
Police released a photo of Lascelles on Sunday and appealed for witnesses to come forward.
"I don't want to comment so much on the viciousness of the scene, it's evidence, but I can say that it was despicable and incredibly cowardly in my view," said Ryan.
"All of her children are with a family friend."
Police say Lascelles was not the father of any of Gangaram's children, who are aged from eight to 14 years old.
Investigators are still reviewing surveillance footage of Lascelles' movements on Friday.
"I'm hoping that we'll learn of Lascelles' whereabouts leading up to the homicide and leading up to him hurling himself in front of a train," Ryan said.
Lascelles is expected to recover from his injuries, but is in "bad shape," Ryan said Sunday.
The community "has been shaken by this senseless act" and these types of "horrible crime scenes" are "grotesquely personal," he added.
Also on HuffPost