Norman has also resigned as a member of the board, the company has announced.
Executive chairman Pat Herbert will take over as an interim CEO until a replacement is found. A recruitment process has already been started.
A spokesperson for the firm was unable to be specific about the reason for Norman's departure. She said the move was to bring about a "change of leadership to take JDR into the next stage of our growth".
Herbert thanked Norman for his contribution to the company during his tenure.
"Following three years of focused investment in the business, JDR is now poised to seize the commercial opportunities that lie ahead," he said.
At the start of September, JDR was handed the contract to design and manufacture inter-array cables for the 402MW Dudgeon offshore project being developed by Statoil and Statkraft.
It was also contracted by Siem Offshore to supply inter-array cables for RWE's 332MW Nordsee 1 project in August.
Earlier this year, the Carbon Trust awarded JDR a share of £400,000 (EUR 503,526) to develop a three-core, 630-square-millimetre, copper conductor, wet design cable. The grant was made to help commercialise the use of 66kV array cables in a bid to decrease costs over an offshore project's lifetime.