The Vos Sailor was damaged and took on water during severe weather overnight.
Coastguard launched a rescue mission after a mayday call at 4.30am and 11 crew members were winched to safety.
Police said one man was fatally injured however. His body has not yet been recovered.
The Vos Sailor, an emergency response and rescue vessel, had been operating on the Balmoral oil field 120 miles off Aberdeen on Scotland's north east coast.
A Grampian Police spokeswoman said: "The vessel sustained significant damage and 11 crew members were winched to safety during an operation co-ordinated by the coastguard in Aberdeen.
"It appears at this time that one crew member has suffered fatal injuries.
"Efforts are ongoing to recover the vessel which will be brought in to Aberdeen harbour in due course."
At the time of the incident, winds in the area were reported to be 60-75 knots with 6.5 metre waves.
Non-essential crew on the nearby North Sea Producer, a floating production, storage and offloading (FPSO) unit, were evacuated to other rigs as a precaution because the disabled boat was drifting.
It is understood the 42.5 metre Vos Sailor may not be recovered until tomorrow.
The vessel is operated by Aberdeen-based Vroon Offshore Services.
A statement on the company's website reads: "Vroon Offshore Services are in the process of contacting the next of kin of the crew of Vos Sailor.
"The company's emergency response team has mustered and - in close co-ordination with the Maritime Coast Guard Agency - is taking all measures to bring the vessel back under control."