One involved a five-and-half-hour trip to Carlisle and another was taken 100 miles away, it is claimed.
Cllr David Brake, head of adult services at Medway Council, said it was "disgusting" patients were being treated this way.
Some mental health patients have to travel hundreds of miles for treatment. Library image.
He said: "Information given to us has shown that one patient went to Hertfordshire and one went to Carlisle."
Cllr Brake was speaking as councillors made a last attempt to stop the closure of mental health facilities at Medway Maritime Hospital.
Kent and Medway NHS Social Care Partnership Trust (KMPT) is closing A Block because the facilities are old and outdated.
"It is always mentally ill people that get hit worse because they are an easy target. It is the Cinderella of the NHS..." - pensioner Brian Clark
Patients will instead be sent to "centres of excellence" being created out of existing wards in Dartford, Maidstone and Canterbury.
KMPT said this will increase beds from 160 to 174 and some of the money saved from A Block's closure will be spent on increasing community services.
But the move has been met with dismay by patients and their families and is opposed by Medway councillors.
Medway Conservatives put forward a motion at last night's full council meeting, calling on NHS commissioners and KMPT to reverse the decision to shut A Block.
The council also plans to write to health secretary Jeremy Hunt, who backed the plan.
Campaigners want to stop the closure of mental health facilities at Medway Maritime Hospital
Cllr Brake said: "I can remember the promises made by KMPT, going back four years now – A Block was going to be brought up to a better standard but they haven't spent a single penny on it - but here they are still able to spend £3.4m sending people out of the area."
Bed shortages meant chiefs spent more than £2million treating patients outside the county between January and July last year.
Cllr David Brake, head of adult services at Medway Council
A report revealed every mental health ward in Kent had been at least 93% full since April 2011 and some at over capacity.
Mr Hunt claimed the provision of care for mental health patients was improving. He said: "Much progress has been made – with mental health patients getting more community-based care and living in their own homes."
Cllr Brake added: "Having heard this statement we now look to Jeremy Hunt to show us what he means. Is he committed to it?"
Pensioner Brian Clark, whose 34-year-old daughter is among the users of A Block, warned that without care in Medway its mentally ill population would struggle.
His daughter has been treated in Maidstone and Canterbury and in just over a week he travelled 600 miles to visit her.
He said: "It is always mentally ill people that get hit worse because they are an easy target. It is the Cinderella of the NHS. If people can't get the help they need they could take their life."
Angela McNab, chief executive of KMPT, said that the closure would "ensure that everyone who needs inpatient mental health crisis care receives it in modern accommodation."