Anas Sarwar, Labour MP for Glasgow Central, said the decision came at a time when the service was trying to cope with a backlog of thousands of cases.
The plans will see 36 jobs lost from the staff of 80 full-time equivalent workforce at Festival Park office in the south of the city.
The cuts are part of a UK-wide exercise by the UK Border Agency to close 40% of the offices and cut 262 jobs.
Mr Sarwar said there was a backlog of 16,000 cases across the service and the cuts would put the remaining staff under even more pressure than at present.
He said: "This announcement is bad news for the staff concerned and bad news for the operation of the Border Agency.
"Cutting the number of decision-makers by half can only mean longer delays to a system which already has a massive backlog.
"It is obvious to anyone who cares to look that the decision to cut staff numbers will put increased pressure on already hard-pressed staff.
"This is nothing more than a cynical cost-cutting exercise."
Union leaders said remaining staff on lower grades will have their targets doubled and warned the changes were not intended to improve the service but to reduce costs.