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.
"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."
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."
She then repeated it as she ran past Canty.
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.