Data from NHS England shows that in the 12 months to September 2018, 54,757 people either did not show up for an outpatient appointment at the trust, or arrived too late to be seen.
With the NHS struggling for funds amid budget cuts and increased demand, the British Medical Association said it was crucial appointments are not wasted while the health service is "under incredible stress".
The average outpatient appointment costs the NHS Â£120, according to the latest resources cost data. This means that the 54,757 missed sessions cost Doncaster and Bassetlaw Teaching Hospitals NHS Foundation Trust around Â£6.57 million.
Dr Robert Harwood, chairman of the BMA's consultant committee, said: "It is important that no appointments are wasted at a time when the NHS is under incredible stress.
"We should not stigmatise patients who may for legitimate reasons be unable to attend.
"However, we do need the NHS to emphasise through clear publicity to the public that, given the current unprecedented pressure, patients should make every possible effort to rearrange their appointment so that another person is able to receive treatment in their place."
At Doncaster and Bassetlaw Teaching Hospitals NHS Foundation Trust, out of the 496,992 outpatient appointments, 11% did not show up.
The figures show 18,589 people failed to make their first appointment, 11% of first attendances.
A further of 36,168, or 11%, did not appear for a subsequent meeting.
Niall Dickson, chief executive of the NHS Confederation, which represents organisations across the healthcare sector, said: "We need to support patients to make sure they can attend appointments, and be able to easily cancel or reschedule them.
"We need to make sure we are not asking patients to attend unnecessary appointments and we welcome the NHS Plan proposal cut face-to-face outpatient appointments by one third over the next five years.
"Text reminders and host of other measures and more technology will make life easier both for patients and the service, but as patients we all need to do our bit."
Across England's health providers, more than 5.8 million appointments were missed in the year to September 2018, which cost the NHS around Â£700 million.
Patients who used London North West University Healthcare trust were the worst at showing up to appointments, while in Cambridge people were the most reliable.