The mother said the man pulled out a knife in front of her daughter at Pak’nSave South Dunedin last Sunday, leaving her daughter terrified and traumatised.
She said as the incident happened her daughter screamed, saying "Stop, I’m too young for this".
When she rushed over, the man holding the knife shouted "you’re never too young for knives".
He then slashed the knife into a stack of boxes next to the 11-year-old, the mother said.
She grabbed her daughter and ran.
While she was pleased with the actions of staff at Pak’nSave, who leapt into action and whisked the pair into another area of the supermarket, she was not impressed with police.
While the man was trespassed by the supermarket, he was let go by police before reviewing CCTV footage and taking any statements from her and her daughter and staff at the supermarket.
A police spokesman told the Otago Daily Times it appeared the man with the knife was not displaying any malicious intent.
The spokesman said an officer spoke to the man, who told them the "child appeared to be trying to get something out of cardboard boxes".
"He offered to help, by using his pocketknife to open the boxes."
The man told officers he had not meant any harm.
He was issued a trespass notice by the supermarket. His knife was not seized as "it is not an offensive or restricted weapon and had not been used to commit criminal offending", police said.
The mother, who saw the knife, said it had a blade larger than the length of her daughter’s face, and it was large and visible in the CCTV footage shown to her by the staff.
The pair went home and the mother returned to the store later in the evening.
"A member of staff came up to me and said ‘look we’re not happy about how that was handled’."
Staff reviewed the CCTV footage and found out the man had spent nine minutes following the pair around the store before presenting his knife.
A member of staff told the mother she should make a complaint to the Independent Police Conduct Authority about how police had handled the situation.
They told her they were also filing a complaint.
"The only supermarket I feel safe shopping at now is Pak’nSave and that is all thanks to the staff."
Her daughter "broke down" at school this week because of what she had experienced, her mother said.
"She’s in counselling now and she’s doing a little better."
The mother was also shaken by the event and had spent days upset and going over what had happened.
"The man never said anything threatening like ‘I’m going to stab you’ — I don’t know what his intention was, but you don’t pull out a knife to a child," she said.
A Foodstuffs spokesman said they were deeply concerned by what had happened.
"The incident was frightening and traumatic for the customer and their child — nobody should have to go through such an ordeal and we’re relieved no-one was hurt.
"While we can’t comment on operational decisions made by police, we trust appropriate procedures were followed and will continue to co-operate with them as needed."