Eltiona Skana, an Albanian national who has paranoid schizophrenia, has been on trial at Manchester Minshull Street Crown Court after pleading not guilty to murder.
Skana has admitted the manslaughter of Emily on the grounds of diminished responsibility.
Yesterday, Skana, 30, was cleared of murder after the prosecution offered no further evidence and withdrew the charge.
Justice Wall will sentence Skana for manslaughter on Tuesday (UK time).
Now her father has recalled the harrowing moment he knew Emily was going to die.
Speaking to the Daily Mail, Jones said he ran towards Emily after the stabbing.
"I was absolutely terrified. I just knew it was so bad. You don't survive these things," he said.
"I just thought, 'Oh my God, I'm going to lose her, I'm going to lose her.'
"I was shouting, 'Just stay with me Emily, stay with me. Don't leave me.'
"She was just trying to breathe. It was just horrific. I wouldn't wish anybody to see that happen to their own daughter. On occasions I will go back there. I try not to.
"But I can just remember her trying to breathe. Just to see your child in that way. I thought, 'This can't be happening. This can't be happening to Emily.'"
Jones said Skana was a "ticking time bomb" who should be locked up for the rest of her life.
"I think she is vile," he said. "How dare she take my child away from me."
"They are just trying to relinquish all responsibility – and she was their responsibility," he said.
"I want the horrible story of what happened to my daughter to be told.
"It was Mother's Day, of all days, when Mum and Dad were in the park with her.
"It's not that I want people to feel sorry for us, but it needs to be told because it's an absolute public outrage."
Attack out of nowhere
Michael Brady QC, who had opened the case for the prosecution, said, "Emily's path towards her mum took her past the defendant who, as Emily scooted by, grabbed her and in one movement slit her throat with the craft knife and then threw her to the ground.
"There had been no interaction between Emily and the defendant. The wound was unsurvivable and Emily died shortly after."
Prior to the attack, a woman – believed to be Skana – had been spotted in the park by a witness who described her as looking "agitated" and a with "vacant" look on her face.
Brady told the court that although Emily's mother was no longer in a relationship with her father she'd gone for a run in the park and had arranged to meet both of them there.
After the attack Skana ran off, still armed with the knife but at some point placed it in her backpack, where it was later recovered.
Brady said passer-by Tony Canty, who was out for a walk with his wife Lynsey and their daughter witnessed Skana "manhandling" and "screaming" at Emily and pushing her to the ground.
Emily's throat was slashed in the park by Eltiona Skana, an Albanian national who has paranoid schizophrenia. Photo / Supplied
Skana was said to have screamed, "She tried to kill me."
At that stage, Canty "had no idea how serous the situation was, he hadn't seen a knife and didn't realise that Emily had been fatally wounded", Brady said.
But he was "sufficiently" concerned to run after Skana, with his wife shouting after him that she had a knife.
He briefly lost sight of Skana but soon caught up with her and either "barged or pushed" her to the ground.
Skana fell on to her back and Canty was able to detain her until the police arrived by sitting on top of her.
Emily's father had seen Skana run off in an "awkward manner" with something "dark and quite long" in her hand.
He went to Emily and saw she was bleeding from the neck and tried to comfort her.
