Louise Chisholm, 29, lost her son Samuel in her womb, but his twin Jack survived. Samuel died from twin transfusion syndrome, a disease of the placenta, and she delivered him along with his healthy brother.
The grieving mother arranged Samuel's funeral at the city's Daldowie Crematorium last October, but was told by staff there were no ashes.
Ms Chisholm, of Glasgow, then urged staff to allow her to lay a small stone in the garden of remembrance next to where her great grandmother's ashes were scattered. However, they said she would have to buy a plot through a hire purchase scheme and a memorial from them. She said: "I can't believe that not only did they throw away my son's ashes and left me with nothing, they refuse to allow me a place where I can grieve for Samuel, somewhere I can take his brother."
A council spokesman said the garden was frequently used by grieving families to scatter ashes and it would be impossible to continue doing this if individual memorial stones were allowed.