Angela Humphrey's body was found in her flat in Quarrywood Avenue, Barmulloch, almost a week after she was last seen.
Ms Humphrey, who lived alone, had only recently moved there to be closer to her family.
The 48-year-old's family was concerned after they hadn't heard from her for five days, and went to her home.
Her daughter's distraught partner and a family friend found her battered body in the living room.
When they realised the mother-of-two was dead, they called 999.
Police today revealed Ms Humphrey, known as Angie, was the victim of a "violent attack" and are now working to trace her last movements.
Detective Inspector Allan Burton urged anyone who may have seen Ms Humphrey since last Friday to contact them.
When asked if he had a message for the killer, the senior detective warned: "I'll be chapping your door soon."
Police Scotland's Major Investigations Team is attempting to establish the motive behind the brutal murder of Ms Humphrey.
Detective Inspector Burton said: "It is possible the person responsible may have been injured, they may have scratches to their face.
"Or they might be acting in a strange manner, please contact police if you have any concerns about family members or anyone you know.
"Angie didn't deserve this. She had a future, a young grandchild and another grandchild on the way.
"Her family have been left devastated and I am determined to catch the person responsible."
Her body was discovered at around 4.40pm on Wednesday.
Ms Humphrey, who has two daughters, was last seen in the Gallowgate area by relatives last Friday afternoon.
Detective Inspector Burton, added: "If you saw Angie, please get in touch.It is not known how she made her way home from the Gallowgate.
"So I would appeal to any taxi drivers who picked up a passenger that matches Angie's description, to get in touch.
"We need to build up a picture of her movements."
Floral tributes left outside Ms Humphrey's home, read: "Rest in peace, Angie, can't believe you're gone.
"Love and miss you always."
Anyone with information is asked to contact Police Scotland on 101.