Eighty one patients were affected on Wednesday by the theft from a back-up generator at Llandough hospital near Cardiff.
Hospital managers said Tuesday's theft of 100m of cabling was "dangerous and irresponsible".
A new back-up generator is being tested before routine surgery can resume.
It was too late for Wednesday's morning list of 36 operations, including two breast cancer operations, which was cancelled as a precaution.
Another 45 operations scheduled for the afternoon were also cancelled after a meeting.
The University Health Board chief executive Jan Williams called the theft "mindless".
She said: "NHS staff work tirelessly to care for some of the most vulnerable members of our communities and it is depressing to note that, for these thieves, the monetary value of copper is of more consequence."
Llandough deals with non-emergency operations, including orthopaedic and breast surgery.
Mrs Williams said the cancellations were "traumatic" for the two breast cancer patients in particular but she said their operations would be rescheduled as quickly as possible.
Health managers are taking steps to provide secondary back-up facilities but these were not in place to allow afternoon operations to take place.
Replacing the cables could cost up to £20,000.
The theft was reported to South Wales Police just after 14.00 GMT on Tuesday.
Councils, public services and utilities have been experiencing rising problems with metal theft nationwide.
Rhondda Cynon Taf Council (RCT) has been working with South Wales Police over the last couple of years to tackle the problem.
The authority's streetcare service director Nigel Wheeler said: "Over the last two years we've had £250,000 worth of copper stolen.
"They'll take anything - goalposts, manhole covers - metal is quite valuable but it costs us more to replace it because of the damage they do.
"Copper theft is the second biggest crime in RCT. There's no quick fix. We need to regulate the scrap yards. Some of legitimate and won't accept copper but there are those that do."
British Transport Police on Wednesday teamed up with other agencies across Wales to launch a crackdown on criminals who trade in stolen metal.
Detective Inspector Mark Cleland said 2011 had been "an unprecedented year in the sheer scale of the problem" despite what were often meagre financial returns.
"What was once seen as a victimless crime is now viewed, in the majority of cases, as one which has a direct impact on hundreds of thousands of people," said Det Insp Cleland.
University Health Board chief executive Jan Williams called the theft 'mindless' and traumatic for patients
Full story can be found here