McLean-based Science Applications International Corp. said Tuesday it plans to cut $350 million in annual costs, primarily by trimming staff and facilities and pushing for greater savings in what it buys.

The company is in the process of splitting itself into two public companies — a roughly $4 billion-a-year services business and an estimated $7 billion-a-year IT company. SAIC officials said Tuesday the split is providing an opportunity to take a closer look at the contractor’s spending and organization.

K. Stuart Shea, chief operating officer of SAIC, said in a call with investors that the contractor plans to cut about $220 million annually by simplifying its organizational structure and cutting administrative or so-called “indirect” staff not tied to specific contracts.

He said SAIC has already trimmed about 800 indirect employees — who typically work in areas like human resources, accounting and payroll — since the split was announced late last summer. Shea said the company will continue to reduce their ranks and seek better efficiency from the part of its workforce working on particular contracts.

Another $70 million in savings will come from reducing SAIC’s facility footprint by about 30 percent, Shea told investors. He said the company is accelerating lease terminations and encouraging employee telework, said Shea.

The contractor also plans to save about $30 million through improving its corporate procurement. This will include, for example, using preferred vendors who provide a discount, according to a spokeswoman.

SAIC officials also noted Tuesday that the company spent $23 million the quarter that ended Jan. 31 on the split, which it has dubbed Project Gemini. The split is expected to be complete sometime between July of this year and January 2014.

The contractor reported profit of $186 million (54 cents per share) for the three-month period ended Jan. 31, up from a loss of $161 million (49 cents) in the same period a year earlier. Last year’s quarterly results reflected a settlement the company paid over CityTime, a troubled employment timekeeping program SAIC managed for New York City.