Frances Simpson, chief executive of Support in Mind Scotland, said the Charlie Reid Centre would have to close by February next year, unless controversial plans to force service users to pay for support are put on hold.
Centre members include people who suffer from symptoms such as psychosis, personality disorder, bi-polar disorder and post traumatic stress disorder, she said.
She said the charity backed the council's policy of self-directed support, giving service users control of the budgets to pay for their care.
However she added: "The pace and nature of implementation in Glasgow, without any consultation with service users or consideration for the impact on people, with the complex and varying nature of mental health problems and mental illness, are putting people at risk."
She said the process appeared to be more about cost-effective commissioning, rather than choice for service users.
The council says it withdrew a grant of £89,000 earlier this year, because it wants to transfer users of the service onto personalised budgets which will allow them to buy a service directly from Support in Mind.
But supporters of the centre say this disregards the fact that mental health problems fluctuate in severity, and does not acknowledge the value of occasional drop-in support.
Ms Simpson said the level of funding was inadequate and the charity was having to support it from its own reserves.
Members have now started an online campaign to save the centre.
Paul Anderson, who has chaired meetings of the campaign group, has used the service regularly for social support and counselling since suffering depression and attempting suicide. He said. "This isn't about personalisation, it is a money-saving measure."
However the council argues that the decision to remove funding from the centre was taken because it provides a social environment for people that does not meet social work objectives. It insists the funding available will ensure the centre can stay open until service users have been assessed for personal budgets, then they can decide for themselves whether to purchase places.
A spokesman said: "This centre provided a low-level service and we believed the money could be spent more effectively elsewhere.
"However, we offered to assess the social care needs of all who attend at the centre and develop personal budgets and care plans with them.
He said they will provide funding for those who use this service while the assessments take place.