Patients had to wait more than two months on average for a hospital appointment in Tayside, official figures show.
There was also a drop in performance at the health board for the proportion of people starting their treatment within 18 weeks of referral (RTT), from 88.4% in June 2017 to 77.2% the same month this year.
And hundreds of patients across Courier Country did not receive diagnostic tests within the six-week target, which are used to detect cancer and other serious diseases, according to the Scottish Government data.
Tayside bosses said it was “not possible” to meet all national targets because of issues including a shortage of consultants and nurses.
The decline in meeting the RTT target in Tayside was the biggest in Scotland over the last year. Only NHS Grampian posted worse figures in June.
The target is for 90% for patients to receive treatment within 18 weeks of referral.
Tayside patients also waited an average of 67 days for a new outpatient appointment, as of June 30 this year, which is by far the longest period in Scotland.
Alex Cole-Hamilton, for the Scottish Liberal Democrats, said: “The Scottish Government must urgently set out how it will turn performance around, given there is no end in sight to the recruitment crisis and staff are run off their feet on every shift.”
Professor Peter Stonebridge, of NHS Tayside, said it was “unfortunately not currently possible to meet the targets across all patient pathways”.
“In Tayside, a number of factors are contributing to this, including a national shortage of consultants in some specialties and vacancies in nursing posts that are hard to fill,” the operational medical director added.
Across Scotland, the number of patients waiting too long for cancer-spotting diagnostic tests has increased by almost 300% in the last two years.
While 87,482 patients needed to have one of eight key diagnostic tests and investigations, as of June 30 this year, 18,644 of them were waiting six weeks or more. That includes 639 patients in Tayside and 180 in Fife.
Gregor McNie, of Cancer Research UK, said: “These statistics suggest that the NHS in Scotland does not have enough staff to be as effective as possible in diagnosing cancer.”
Labour health spokesman Anas Sarwar said: “Performance for key clinical tests simply has to improve – early detection saves lives.”
Health Secretary Jeane Freeman said: “Meeting the challenge of improving performance and reducing waits requires the twin approach of investment and reform.
“That’s why we recently allocated an additional £6 million to reduce waiting times for endoscopies, with a focus on the most urgent patients, including those with suspected cancer.”